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class="vector-toc-link" href="#Complexity_of_cities"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Complexity of cities</span> </div> </a> <ul id="toc-Complexity_of_cities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_economics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complexity_economics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Complexity economics</span> </div> </a> <ul id="toc-Complexity_economics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_and_education" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complexity_and_education"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Complexity and education</span> </div> </a> <ul id="toc-Complexity_and_education-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_in_healthcare_research_and_practice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complexity_in_healthcare_research_and_practice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Complexity in healthcare research and practice</span> </div> </a> <ul id="toc-Complexity_in_healthcare_research_and_practice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_and_biology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complexity_and_biology"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Complexity and biology</span> </div> </a> <ul id="toc-Complexity_and_biology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_and_chaos_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complexity_and_chaos_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Complexity and chaos theory</span> </div> </a> <ul id="toc-Complexity_and_chaos_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complexity_and_network_science" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complexity_and_network_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Complexity and network science</span> </div> </a> <ul id="toc-Complexity_and_network_science-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Notable_scholars" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notable_scholars"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notable scholars</span> </div> </a> <ul id="toc-Notable_scholars-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " 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Available in 35 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-35" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">35 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Komplekse_stelsel" title="Komplekse stelsel – Afrikaans" lang="af" hreflang="af" data-title="Komplekse stelsel" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%A7%D9%85_%D9%85%D8%B9%D9%82%D8%AF" title="نظام معقد – Arabic" lang="ar" hreflang="ar" data-title="نظام معقد" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9C%E0%A6%9F%E0%A6%BF%E0%A6%B2_%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%AC%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BE" title="জটিল ব্যবস্থা – Bangla" lang="bn" hreflang="bn" data-title="জটিল ব্যবস্থা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B8" title="Комплексни системи – Bulgarian" lang="bg" hreflang="bg" data-title="Комплексни системи" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Sistema_complex" title="Sistema complex – Catalan" lang="ca" hreflang="ca" data-title="Sistema complex" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Komplexn%C3%AD_syst%C3%A9m" title="Komplexní systém – Czech" lang="cs" hreflang="cs" data-title="Komplexní systém" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Komplekst_system" title="Komplekst system – Danish" lang="da" hreflang="da" data-title="Komplekst system" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Komplexes_System" title="Komplexes System – German" lang="de" hreflang="de" data-title="Komplexes System" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Komplekss%C3%BCsteem" title="Komplekssüsteem – Estonian" lang="et" hreflang="et" data-title="Komplekssüsteem" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Sistema_complejo" title="Sistema complejo – Spanish" lang="es" hreflang="es" data-title="Sistema complejo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%A7%D9%85%D8%A7%D9%86%D9%87_%D9%BE%DB%8C%DA%86%DB%8C%D8%AF%D9%87" title="سامانه پیچیده – Persian" lang="fa" hreflang="fa" data-title="سامانه پیچیده" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_complexe" title="Système complexe – French" lang="fr" hreflang="fr" data-title="Système complexe" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Sistema_complexo" title="Sistema complexo – Galician" lang="gl" hreflang="gl" data-title="Sistema complexo" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%B5%EC%9E%A1%EA%B3%84" title="복잡계 – Korean" lang="ko" hreflang="ko" data-title="복잡계" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9C%E0%A4%9F%E0%A4%BF%E0%A4%B2_%E0%A4%A4%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="जटिल तंत्र – Hindi" lang="hi" hreflang="hi" data-title="जटिल तंत्र" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Komplexa_sistemo" title="Komplexa sistemo – Ido" lang="io" hreflang="io" data-title="Komplexa sistemo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sistem_kompleks" title="Sistem kompleks – Indonesian" lang="id" hreflang="id" data-title="Sistem kompleks" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Sistema_complesso" title="Sistema complesso – Italian" lang="it" hreflang="it" data-title="Sistema complesso" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%A8%D7%9B%D7%AA_%D7%9E%D7%95%D7%A8%D7%9B%D7%91%D7%AA" title="מערכת מורכבת – Hebrew" lang="he" hreflang="he" data-title="מערכת מורכבת" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D2%AF%D1%80%D0%B4%D0%B5%D0%BB%D1%96_%D0%B6%D2%AF%D0%B9%D0%B5" title="Күрделі жүйе – Kazakh" lang="kk" hreflang="kk" data-title="Күрделі жүйе" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kompleksa_sist%C4%93ma" title="Kompleksa sistēma – Latvian" lang="lv" hreflang="lv" data-title="Kompleksa sistēma" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Complex_systeem" title="Complex systeem – Dutch" lang="nl" hreflang="nl" data-title="Complex systeem" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A4%87%E9%9B%91%E7%B3%BB" title="複雑系 – Japanese" lang="ja" hreflang="ja" data-title="複雑系" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/System_z%C5%82o%C5%BCony" title="System złożony – Polish" lang="pl" hreflang="pl" data-title="System złożony" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistemas_complexos" title="Sistemas complexos – Portuguese" lang="pt" hreflang="pt" data-title="Sistemas complexos" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B6%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Сложная система – Russian" lang="ru" hreflang="ru" data-title="Сложная система" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Complex_system" title="Complex system – Simple English" lang="en-simple" hreflang="en-simple" data-title="Complex system" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%DB%8C%D8%B3%D8%AA%D9%85%DB%8C_%D8%A6%D8%A7%DA%B5%DB%86%D8%B2" title="سیستمی ئاڵۆز – Central Kurdish" lang="ckb" hreflang="ckb" data-title="سیستمی ئاڵۆز" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Monimutkainen_j%C3%A4rjestelm%C3%A4" title="Monimutkainen järjestelmä – Finnish" lang="fi" hreflang="fi" data-title="Monimutkainen järjestelmä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Komplexa_system" title="Komplexa system – Swedish" lang="sv" hreflang="sv" data-title="Komplexa system" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Karma%C5%9F%C4%B1k_sistem" title="Karmaşık sistem – Turkish" lang="tr" hreflang="tr" data-title="Karmaşık sistem" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Складна система – Ukrainian" lang="uk" hreflang="uk" data-title="Складна система" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_th%E1%BB%91ng_ph%E1%BB%A9c_t%E1%BA%A1p" title="Hệ thống phức tạp – Vietnamese" lang="vi" hreflang="vi" data-title="Hệ thống phức tạp" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%A4%87%E9%9B%9C%E7%B3%BB%E7%B5%B1" title="複雜系統 – Cantonese" lang="yue" hreflang="yue" data-title="複雜系統" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%8D%E6%9D%82%E7%B3%BB%E7%BB%9F" title="复杂系统 – Chinese" lang="zh" hreflang="zh" data-title="复杂系统" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q854457#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Complex_system" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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<div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">System composed of many interacting components</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Complex systems" redirects here. 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screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a class="mw-selflink selflink">Complex systems</a></th></tr><tr><th class="sidebar-heading"> Topics</th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Emergence" title="Emergence">Emergence</a><br /></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Collective_behavior" title="Collective behavior">Collective behavior</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Social_dynamics" title="Social dynamics">Social dynamics</a><br /> <p><a 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href="/wiki/Collective_consciousness" title="Collective consciousness">Collective consciousness</a><br /></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Network_science" title="Network science">Networks</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Scale-free_network" title="Scale-free network">Scale-free networks</a><br /> <p><a href="/wiki/Social_network_analysis" title="Social network analysis">Social network analysis</a><br /> <a href="/wiki/Small-world_network" title="Small-world network">Small-world networks</a><br /> <a href="/wiki/Centrality" title="Centrality">Centrality</a><br /> <a href="/wiki/Network_motif" title="Network motif">Motifs</a><br /> <a href="/wiki/Graph_theory" title="Graph theory">Graph theory</a><br /> <a href="/wiki/Scalability" title="Scalability">Scaling</a><br /> <a href="/wiki/Robustness_(computer_science)" title="Robustness (computer science)">Robustness</a><br /> <a href="/wiki/Systems_biology" title="Systems biology">Systems biology</a><br /> <a href="/wiki/Dynamic_network_analysis" title="Dynamic network analysis">Dynamic networks</a><br /> </p> <a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">Adaptive networks</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Evolution" title="Evolution">Evolution</a> and <a href="/wiki/Adaptation" title="Adaptation">adaptation</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural network</a><br /> <p><a href="/wiki/Evolutionary_computation" title="Evolutionary computation">Evolutionary computation</a><br /> <a href="/wiki/Genetic_algorithm" title="Genetic algorithm">Genetic algorithms</a><br /> <a href="/wiki/Genetic_programming" title="Genetic programming">Genetic programming</a><br /> <a href="/wiki/Artificial_life" title="Artificial life">Artificial life</a><br /> <a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a><br /> <a href="/wiki/Evolutionary_developmental_biology" title="Evolutionary developmental biology">Evolutionary developmental biology</a><br /> <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</a><br /> <a href="/wiki/Evolutionary_robotics" title="Evolutionary robotics">Evolutionary robotics</a><br /> </p> <a href="/wiki/Evolvability" title="Evolvability">Evolvability</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Pattern_formation" title="Pattern formation">Pattern formation</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Fractal" title="Fractal">Fractals</a><br /> <p><a href="/wiki/Reaction%E2%80%93diffusion_system" title="Reaction–diffusion system">Reaction–diffusion systems</a><br /> <a href="/wiki/Partial_differential_equation" title="Partial differential equation">Partial differential equations</a><br /> <a href="/wiki/Dissipative_system" title="Dissipative system">Dissipative structures</a><br /> <a href="/wiki/Percolation" title="Percolation">Percolation</a><br /> <a href="/wiki/Cellular_automaton" title="Cellular automaton">Cellular automata</a><br /> <a href="/wiki/Spatial_ecology" title="Spatial ecology">Spatial ecology</a><br /> <a href="/wiki/Self-replication" title="Self-replication">Self-replication</a><br /> </p> <a href="/wiki/Geomorphology" title="Geomorphology">Geomorphology</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Systems_theory" title="Systems theory">Systems theory</a> and <a href="/wiki/Cybernetics" title="Cybernetics">cybernetics</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Autopoiesis" title="Autopoiesis">Autopoiesis</a><br /> <p><a href="/wiki/Conversation_theory" title="Conversation theory">Conversation theory</a><br /> <a href="/wiki/Entropy" title="Entropy">Entropy</a><br /> <a href="/wiki/Feedback" title="Feedback">Feedback</a> <br /> <a href="/wiki/Goal_orientation" title="Goal orientation">Goal-oriented</a><br /> <a href="/wiki/Homeostasis" title="Homeostasis">Homeostasis</a> <br /> <a href="/wiki/Information_theory" title="Information theory">Information theory</a><br /> <a href="/wiki/Operationalization" title="Operationalization">Operationalization</a><br /> <a href="/wiki/Second-order_cybernetics" title="Second-order cybernetics">Second-order cybernetics</a><br /> <a href="/wiki/Self-reference" title="Self-reference">Self-reference</a><br /> <a href="/wiki/System_dynamics" title="System dynamics">System dynamics</a><br /> <a href="/wiki/Systems_science" title="Systems science">Systems science</a><br /> <a href="/wiki/Systems_thinking" title="Systems thinking">Systems thinking</a><br /> <a href="/wiki/Sensemaking" title="Sensemaking">Sensemaking</a><br /> <a href="/wiki/Variety_(cybernetics)" title="Variety (cybernetics)">Variety</a><br /> </p> <a href="/wiki/Theory_of_computation" title="Theory of computation">Theory of computation</a><br /></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Nonlinear_system" title="Nonlinear system">Nonlinear dynamics</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Time_series" title="Time series">Time series analysis</a><br /> <p><a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">Ordinary differential equations</a><br /> <a href="/wiki/Phase_space" title="Phase space">Phase space</a><br /> <a href="/wiki/Attractor" title="Attractor">Attractors</a><br /> <a href="/wiki/Population_dynamics" title="Population dynamics">Population dynamics</a><br /> <a href="/wiki/Chaos_theory" title="Chaos theory">Chaos</a><br /> <a href="/wiki/Multistability" title="Multistability">Multistability</a><br /> <a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation</a><br /> </p> <a href="/wiki/Coupled_map_lattice" title="Coupled map lattice">Coupled map lattices</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Game_theory" title="Game theory">Game theory</a></div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">Prisoner's dilemma</a><br /> <p><a href="/wiki/Rational_choice_theory" class="mw-redirect" title="Rational choice theory">Rational choice theory</a><br /> <a href="/wiki/Bounded_rationality" title="Bounded rationality">Bounded rationality</a><br /> </p> <a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">Evolutionary game theory</a><br /></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Complex_systems" title="Template:Complex systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Complex_systems" title="Template talk:Complex systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Complex_systems" title="Special:EditPage/Template:Complex systems"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <b>complex system</b> is a <a href="/wiki/System" title="System">system</a> composed of many components which may interact with each other.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Examples of complex systems are Earth's global <a href="/wiki/Climate" title="Climate">climate</a>, <a href="/wiki/Organisms" class="mw-redirect" title="Organisms">organisms</a>, the <a href="/wiki/Human_brain" title="Human brain">human brain</a>, infrastructure such as power grid, transportation or communication systems, complex <a href="/wiki/Software" title="Software">software</a> and electronic systems, social and economic organizations (like <a href="/wiki/Cities" class="mw-redirect" title="Cities">cities</a>), an <a href="/wiki/Ecosystem" title="Ecosystem">ecosystem</a>, a living <a href="/wiki/Cell_(biology)" title="Cell (biology)">cell</a>, and, ultimately, for some authors, the entire <a href="/wiki/Universe" title="Universe">universe</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The behavior of a complex system is intrinsically difficult to model due to the dependencies, competitions, relationships, and other types of interactions between their parts or between a given system and its environment.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Systems that are "<a href="/wiki/Complexity" title="Complexity">complex</a>" have distinct properties that arise from these relationships, such as <a href="/wiki/Nonlinear_system" title="Nonlinear system">nonlinearity</a>, <a href="/wiki/Emergence" title="Emergence">emergence</a>, <a href="/wiki/Spontaneous_order" title="Spontaneous order">spontaneous order</a>, <a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">adaptation</a>, and <a href="/wiki/Feedback" title="Feedback">feedback loops</a>, among others.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links represent their interactions. </p><p>The term <i>complex systems</i> often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to <a href="/wiki/Reductionism" title="Reductionism">reductionism</a>, which attempts to explain systems in terms of their constituent parts and the individual interactions between them. </p><p>As an interdisciplinary domain, complex systems draw contributions from many different fields, such as the study of <a href="/wiki/Self-organization" title="Self-organization">self-organization</a> and critical phenomena from physics, of <a href="/wiki/Spontaneous_order" title="Spontaneous order">spontaneous order</a> from the social sciences, <a href="/wiki/Chaos_theory" title="Chaos theory">chaos</a> from mathematics, <a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">adaptation</a> from biology, and many others. <i>Complex systems</i> is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including <a href="/wiki/Statistical_physics" class="mw-redirect" title="Statistical physics">statistical physics</a>, <a href="/wiki/Information_theory" title="Information theory">information theory</a>, <a href="/wiki/Nonlinear_system" title="Nonlinear system">nonlinear dynamics</a>, <a href="/wiki/Anthropology" title="Anthropology">anthropology</a>, <a href="/wiki/Computer_science" title="Computer science">computer science</a>, <a href="/wiki/Meteorology" title="Meteorology">meteorology</a>, <a href="/wiki/Sociology" title="Sociology">sociology</a>, <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Psychology" title="Psychology">psychology</a>, and <a href="/wiki/Biology" title="Biology">biology</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Key_concepts">Key concepts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=1" title="Edit section: Key concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Adaptation">Adaptation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=2" title="Edit section: Adaptation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">Complex adaptive systems</a> are special cases of complex systems that are <a href="/wiki/Adaptive_system" title="Adaptive system">adaptive</a> in that they have the capacity to change and learn from experience.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Examples of complex adaptive systems include the international <a href="/wiki/Trade" title="Trade">trade</a> markets, social insect and <a href="/wiki/Ant" title="Ant">ant</a> colonies, the <a href="/wiki/Biosphere" title="Biosphere">biosphere</a> and the <a href="/wiki/Ecosystem" title="Ecosystem">ecosystem</a>, the <a href="/wiki/Human_brain" title="Human brain">brain</a> and the <a href="/wiki/Immune_system" title="Immune system">immune system</a>, the <a href="/wiki/Cell_(biology)" title="Cell (biology)">cell</a> and the developing <a href="/wiki/Embryo" title="Embryo">embryo</a>, cities, <a href="/wiki/Manufacturing" title="Manufacturing">manufacturing businesses</a> and any human social group-based endeavor in a cultural and <a href="/wiki/Social_system" title="Social system">social system</a> such as <a href="/wiki/Political_party" title="Political party">political parties</a> or <a href="/wiki/Community" title="Community">communities</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Features">Features</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=3" title="Edit section: Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Complex systems may have the following features:<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <dl><dt>Complex systems may be open</dt> <dd>Complex systems are usually <a href="/wiki/Open_system_(systems_theory)" title="Open system (systems theory)">open systems</a> – that is, they exist in a <a href="/wiki/Thermodynamic" class="mw-redirect" title="Thermodynamic">thermodynamic</a> gradient and dissipate energy. In other words, complex systems are frequently far from energetic <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">equilibrium</a>: but despite this flux, there may be <a href="/w/index.php?title=Pattern_stability&action=edit&redlink=1" class="new" title="Pattern stability (page does not exist)">pattern stability</a>,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> see <a href="/wiki/Synergetics_(Haken)" title="Synergetics (Haken)">synergetics</a>.</dd></dl> <dl><dt>Complex systems may exhibit critical transitions</dt></dl> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Alternative_stable_states,_critical_transitions,_and_the_direction_of_critical_slowing_down.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Alternative_stable_states%2C_critical_transitions%2C_and_the_direction_of_critical_slowing_down.png/220px-Alternative_stable_states%2C_critical_transitions%2C_and_the_direction_of_critical_slowing_down.png" decoding="async" width="220" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Alternative_stable_states%2C_critical_transitions%2C_and_the_direction_of_critical_slowing_down.png/330px-Alternative_stable_states%2C_critical_transitions%2C_and_the_direction_of_critical_slowing_down.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Alternative_stable_states%2C_critical_transitions%2C_and_the_direction_of_critical_slowing_down.png/440px-Alternative_stable_states%2C_critical_transitions%2C_and_the_direction_of_critical_slowing_down.png 2x" data-file-width="500" data-file-height="403" /></a><figcaption>Graphical representation of alternative stable states and the direction of critical slowing down prior to a critical transition (taken from Lever et al. 2020).<sup id="cite_ref-auto11_12-0" class="reference"><a href="#cite_note-auto11-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Top panels (a) indicate stability landscapes at different conditions. Middle panels (b) indicate the rates of change akin to the slope of the stability landscapes, and bottom panels (c) indicate a recovery from a perturbation towards the system's future state (c.I) and in another direction (c.II).</figcaption></figure> <dl><dd><a href="/wiki/Critical_transition" title="Critical transition">Critical transitions</a> are abrupt shifts in the state of <a href="/wiki/Ecosystem" title="Ecosystem">ecosystems</a>, the <a href="/wiki/Climate" title="Climate">climate</a>, financial and economic systems or other complex systems that may occur when changing conditions pass a critical or <a href="/wiki/Bifurcation_theory" title="Bifurcation theory">bifurcation point</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The 'direction of critical slowing down' in a system's state space may be indicative of a system's future state after such transitions when delayed negative feedbacks leading to oscillatory or other complex dynamics are weak.<sup id="cite_ref-auto11_12-1" class="reference"><a href="#cite_note-auto11-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></dd></dl> <dl><dt>Complex systems may be <a href="/wiki/Hierarchy#Nested_hierarchy" title="Hierarchy">nested</a></dt> <dd>The components of a complex system may themselves be complex systems. For example, an <a href="/wiki/Economics" title="Economics">economy</a> is made up of <a href="/wiki/Organisation" class="mw-redirect" title="Organisation">organisations</a>, which are made up of <a href="/wiki/Person" title="Person">people</a>, which are made up of <a href="/wiki/Cell_(biology)" title="Cell (biology)">cells</a> – all of which are complex systems. The arrangement of interactions within complex bipartite networks may be nested as well. More specifically, bipartite ecological and organisational networks of mutually beneficial interactions were found to have a nested structure.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> This structure promotes indirect facilitation and a system's capacity to persist under increasingly harsh circumstances as well as the potential for large-scale systemic regime shifts.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></dd></dl> <dl><dt>Dynamic network of multiplicity</dt> <dd>As well as <a href="/wiki/Coupling" title="Coupling">coupling</a> rules, the dynamic <a href="/wiki/Biological_network" title="Biological network">network</a> of a complex system is important. <a href="/wiki/Small-world_network" title="Small-world network">Small-world</a> or <a href="/wiki/Scale-free_network" title="Scale-free network">scale-free</a> networks<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> which have many local interactions and a smaller number of inter-area connections are often employed. Natural complex systems often exhibit such topologies. In the human <a href="/wiki/Cerebral_cortex" title="Cerebral cortex">cortex</a> for example, we see dense local connectivity and a few very long <a href="/wiki/Axonal" class="mw-redirect" title="Axonal">axon</a> projections between regions inside the cortex and to other brain regions.</dd></dl> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:Gospers_glider_gun.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/e/e5/Gospers_glider_gun.gif" decoding="async" width="250" height="180" class="mw-file-element" data-file-width="250" data-file-height="180" /></a><figcaption><a href="/wiki/Bill_Gosper" title="Bill Gosper">Gosper's</a> <a href="/wiki/Gun_(cellular_automaton)" title="Gun (cellular automaton)">Glider Gun</a> creating "<a href="/wiki/Glider_(Conway%27s_Life)" class="mw-redirect" title="Glider (Conway's Life)">gliders</a>" in the cellular automaton <a href="/wiki/Conway%27s_Game_of_Life" title="Conway's Game of Life">Conway's Game of Life</a><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></figcaption></figure> <dl><dt>May produce emergent phenomena</dt> <dd>Complex systems may exhibit behaviors that are <a href="/wiki/Emergence" title="Emergence">emergent</a>, which is to say that while the results may be sufficiently determined by the activity of the systems' basic constituents, they may have properties that can only be studied at a higher level. For example, empirical food webs display regular, scale-invariant features across aquatic and terrestrial ecosystems when studied at the level of clustered 'trophic' species.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Another example is offered by the <a href="/wiki/Termites" class="mw-redirect" title="Termites">termites</a> in a mound which have physiology, biochemistry and biological development at one level of analysis, whereas their <a href="/wiki/Social_behavior" title="Social behavior">social behavior</a> and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level.</dd></dl> <dl><dt>Relationships are non-linear</dt> <dd>In practical terms, this means a small perturbation may cause a large effect (see <a href="/wiki/Butterfly_effect" title="Butterfly effect">butterfly effect</a>), a proportional effect, or even no effect at all. In linear systems, the effect is <i>always</i> directly proportional to cause. See <a href="/wiki/Nonlinearity" class="mw-redirect" title="Nonlinearity">nonlinearity</a>.</dd></dl> <dl><dt>Relationships contain feedback loops</dt> <dd>Both negative (<a href="/wiki/Damping_ratio" class="mw-redirect" title="Damping ratio">damping</a>) and positive (amplifying) <a href="/wiki/Feedback" title="Feedback">feedback</a> are always found in complex systems. The effects of an element's behavior are fed back in such a way that the element itself is altered.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=4" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1948, Dr. Warren Weaver published an essay on "Science and Complexity",<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> exploring the diversity of problem types by contrasting problems of simplicity, disorganized complexity, and organized complexity. Weaver described these as "problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole." </p><p>While the explicit study of complex systems dates at least to the 1970s,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> the first research institute focused on complex systems, the <a href="/wiki/Santa_Fe_Institute" title="Santa Fe Institute">Santa Fe Institute</a>, was founded in 1984.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Early Santa Fe Institute participants included physics Nobel laureates <a href="/wiki/Murray_Gell-Mann" title="Murray Gell-Mann">Murray Gell-Mann</a> and <a href="/wiki/Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Philip Anderson</a>, economics Nobel laureate <a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a>, and Manhattan Project scientists <a href="/wiki/George_Cowan" title="George Cowan">George Cowan</a> and <a href="/wiki/Herbert_L._Anderson" title="Herbert L. Anderson">Herb Anderson</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Today, there are over 50 institutes and research centers focusing on complex systems.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2019)">citation needed</span></a></i>]</sup> </p><p>Since the late 1990s, the interest of mathematical physicists in researching economic phenomena has been on the rise. The proliferation of cross-disciplinary research with the application of solutions originated from the physics epistemology has entailed a gradual paradigm shift in the theoretical articulations and methodological approaches in economics, primarily in financial economics. The development has resulted in the emergence of a new branch of discipline, namely "econophysics", which is broadly defined as a cross-discipline that applies statistical physics methodologies which are mostly based on the complex systems theory and the chaos theory for economics analysis.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>The 2021 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> was awarded to <a href="/wiki/Syukuro_Manabe" title="Syukuro Manabe">Syukuro Manabe</a>, <a href="/wiki/Klaus_Hasselmann" title="Klaus Hasselmann">Klaus Hasselmann</a>, and <a href="/wiki/Giorgio_Parisi" title="Giorgio Parisi">Giorgio Parisi</a> for their work to understand complex systems. Their work was used to create more accurate computer models of the effect of global warming on the Earth's climate.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=5" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Complexity_in_practice">Complexity in practice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=6" title="Edit section: Complexity in practice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The traditional approach to dealing with complexity is to reduce or constrain it. Typically, this involves compartmentalization: dividing a large system into separate parts. Organizations, for instance, divide their work into departments that each deal with separate issues. Engineering systems are often designed using modular components. However, modular designs become susceptible to failure when issues arise that bridge the divisions. </p> <div class="mw-heading mw-heading3"><h3 id="Complexity_of_cities">Complexity of cities</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=7" title="Edit section: Complexity of cities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jane Jacobs described cities as being a problem in organized complexity in 1961, citing Dr. Weaver's 1948 essay.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> As an example, she explains how an abundance of factors interplay into how various urban spaces lead to a diversity of interactions, and how changing those factors can change how the space is used, and how well the space supports the functions of the city. She further illustrates how cities have been severely damaged when approached as a problem in simplicity by replacing organized complexity with simple and predictable spaces, such as Le Corbusier's "Radiant City" and Ebenezer Howard's "Garden City". Since then, others have written at length on the complexity of cities.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complexity_economics">Complexity economics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=8" title="Edit section: Complexity economics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Over the last decades, within the emerging field of <a href="/wiki/Complexity_economics" title="Complexity economics">complexity economics</a>, new predictive tools have been developed to explain economic growth. Such is the case with the models built by the <a href="/wiki/Santa_Fe_Institute" title="Santa Fe Institute">Santa Fe Institute</a> in 1989 and the more recent <a href="/wiki/Economic_complexity_index" title="Economic complexity index">economic complexity index</a> (ECI), introduced by the <a href="/wiki/MIT" class="mw-redirect" title="MIT">MIT</a> physicist <a href="/wiki/Cesar_A._Hidalgo" class="mw-redirect" title="Cesar A. Hidalgo">Cesar A. Hidalgo</a> and the <a href="/wiki/Harvard" class="mw-redirect" title="Harvard">Harvard</a> economist <a href="/wiki/Ricardo_Hausmann" title="Ricardo Hausmann">Ricardo Hausmann</a>. </p><p><a href="/wiki/Recurrence_quantification_analysis" title="Recurrence quantification analysis">Recurrence quantification analysis</a> has been employed to detect the characteristic of <a href="/wiki/Business_cycles" class="mw-redirect" title="Business cycles">business cycles</a> and <a href="/wiki/Economic_development" title="Economic development">economic development</a>. To this end, Orlando et al.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> developed the so-called recurrence quantification correlation index (RQCI) to test correlations of RQA on a sample signal and then investigated the application to business time series. The said index has been proven to detect hidden changes in time series. Further, Orlando et al.,<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> over an extensive dataset, shown that recurrence quantification analysis may help in anticipating transitions from laminar (i.e. regular) to turbulent (i.e. chaotic) phases such as USA GDP in 1949, 1953, etc. Last but not least, it has been demonstrated that recurrence quantification analysis can detect differences between macroeconomic variables and highlight hidden features of economic dynamics. </p> <div class="mw-heading mw-heading3"><h3 id="Complexity_and_education">Complexity and education</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=9" title="Edit section: Complexity and education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Focusing on issues of student persistence with their studies, Forsman, Moll and Linder explore the "viability of using complexity science as a frame to extend methodological applications for physics education research", finding that "framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics".<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complexity_in_healthcare_research_and_practice">Complexity in healthcare research and practice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=10" title="Edit section: Complexity in healthcare research and practice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Healthcare systems are prime examples of complex systems, characterized by interactions among diverse stakeholders, such as patients, providers, policymakers, and researchers, across various sectors like health, government, community, and education. These systems demonstrate properties like non-linearity, emergence, adaptation, and feedback loops.<sup id="cite_ref-:0_38-0" class="reference"><a href="#cite_note-:0-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Complexity science in healthcare frames <a href="/wiki/Knowledge_translation" title="Knowledge translation">knowledge translation</a> as a dynamic and interconnected network of processes—problem identification, knowledge creation, synthesis, implementation, and evaluation—rather than a linear or cyclical sequence. Such approaches emphasize the importance of understanding and leveraging the interactions within and between these processes and stakeholders to optimize the creation and movement of knowledge. By acknowledging the complex, adaptive nature of healthcare systems, <a href="/wiki/Complexity_Science" class="mw-redirect" title="Complexity Science">complexity science</a> advocates for continuous stakeholder engagement, <a href="/wiki/Transdisciplinary" class="mw-redirect" title="Transdisciplinary">transdisciplinary</a> collaboration, and flexible strategies to effectively translate research into practice.<sup id="cite_ref-:0_38-1" class="reference"><a href="#cite_note-:0-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complexity_and_biology">Complexity and biology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=11" title="Edit section: Complexity and biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Complexity science has been applied to living organisms, and in particular to biological systems. Within the emerging field of <a href="/wiki/Fractal_physiology" title="Fractal physiology">fractal physiology</a>, bodily signals, such as heart rate or brain activity, are characterized using <a href="/wiki/Entropy" title="Entropy">entropy</a> or fractal indices. The goal is often to assess the state and the health of the underlying system, and diagnose potential disorders and illnesses.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2024)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complexity_and_chaos_theory">Complexity and chaos theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=12" title="Edit section: Complexity and chaos theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Complex systems theory is related to <a href="/wiki/Chaos_theory" title="Chaos theory">chaos theory</a>, which in turn has its origins more than a century ago in the work of the French mathematician <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions of the system, though in practice this is impossible to do with arbitrary accuracy. </p><p>The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex.<sup id="cite_ref-PC98_40-0" class="reference"><a href="#cite_note-PC98-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> This is referred to as the "<a href="/wiki/Edge_of_chaos" title="Edge of chaos">edge of chaos</a>".<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Lorenz_attractor_yb.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Lorenz_attractor_yb.svg/200px-Lorenz_attractor_yb.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Lorenz_attractor_yb.svg/300px-Lorenz_attractor_yb.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Lorenz_attractor_yb.svg/400px-Lorenz_attractor_yb.svg.png 2x" data-file-width="750" data-file-height="750" /></a><figcaption>A plot of the <a href="/wiki/Lorenz_attractor" class="mw-redirect" title="Lorenz attractor">Lorenz attractor</a></figcaption></figure> <p>When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as it is within chaos theory, in which it prevails. As stated by Colander,<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.<sup id="cite_ref-PC98_40-1" class="reference"><a href="#cite_note-PC98-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> For recent examples in economics and business see Stoop et al.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> who discussed <a href="/wiki/Android_(operating_system)" title="Android (operating system)">Android</a>'s market position, Orlando<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> who explained the corporate dynamics in terms of mutual synchronization and chaos regularization of bursts in a group of chaotically bursting cells and Orlando et al.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> who modelled financial data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity) with a low-dimensional deterministic model. </p><p>Therefore, the main difference between chaotic systems and complex systems is their history.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Chaotic systems do not rely on their history as complex ones do. Chaotic behavior pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (September 2011)">clarification needed</span></a></i>]</sup> On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist <a href="/wiki/Murray_Gell-Mann" title="Murray Gell-Mann">Murray Gell-Mann</a> called "an accumulation of frozen accidents".<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations. </p> <div style="clear:left;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Complexity_and_network_science">Complexity and network science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=13" title="Edit section: Complexity and network science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A complex system is usually composed of many components and their interactions. Such a system can be represented by a network where nodes represent the components and links represent their interactions.<sup id="cite_ref-DorogovtsevMendes2003_48-0" class="reference"><a href="#cite_note-DorogovtsevMendes2003-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Newman2010_49-0" class="reference"><a href="#cite_note-Newman2010-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> For example, the <a href="/wiki/Internet" title="Internet">Internet</a> can be represented as a network composed of nodes (computers) and links (direct connections between computers). Other examples of complex networks include social networks, financial institution interdependencies,<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> airline networks,<sup id="cite_ref-BarratBarthelemy2004_51-0" class="reference"><a href="#cite_note-BarratBarthelemy2004-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> and biological networks. </p> <div class="mw-heading mw-heading2"><h2 id="Notable_scholars">Notable scholars</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=14" title="Edit section: Notable scholars"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Robert_McCormick_Adams_Jr." title="Robert McCormick Adams Jr.">Robert McCormick Adams</a></li> <li><a href="/wiki/Christopher_Alexander" title="Christopher Alexander">Christopher Alexander</a></li> <li><a href="/wiki/Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Philip Anderson</a></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a></li> <li><a href="/wiki/Robert_Axelrod_(political_scientist)" title="Robert Axelrod (political scientist)">Robert Axelrod</a></li> <li><a href="/wiki/W._Brian_Arthur" title="W. Brian Arthur">W. Brian Arthur</a></li> <li><a href="/wiki/Per_Bak" title="Per Bak">Per Bak</a></li> <li><a href="/wiki/B%C3%A9la_H._B%C3%A1n%C3%A1thy" title="Béla H. Bánáthy">Béla H. Bánáthy</a></li> <li><a href="/wiki/Albert-L%C3%A1szl%C3%B3_Barab%C3%A1si" title="Albert-László Barabási">Albert-Laszlo Barabasi</a></li> <li><a href="/wiki/Yaneer_Bar-Yam" title="Yaneer Bar-Yam">Yaneer Bar-Yam</a></li> <li><a href="/wiki/Gregory_Bateson" title="Gregory Bateson">Gregory Bateson</a></li> <li><a href="/wiki/Ludwig_von_Bertalanffy" title="Ludwig von Bertalanffy">Ludwig von Bertalanffy</a></li> <li><a href="/wiki/Alexander_Bogdanov" title="Alexander Bogdanov">Alexander Bogdanov</a></li> <li><a href="/wiki/Samuel_Bowles_(economist)" title="Samuel Bowles (economist)">Samuel Bowles</a></li> <li><a href="/wiki/Guido_Caldarelli" title="Guido Caldarelli">Guido Caldarelli</a></li> <li><a href="/wiki/Paul_Cilliers" title="Paul Cilliers">Paul Cilliers</a></li> <li><a href="/wiki/Walter_Clemens,_Jr." class="mw-redirect" title="Walter Clemens, Jr.">Walter Clemens, Jr.</a></li> <li><a href="/wiki/James_P._Crutchfield" title="James P. Crutchfield">James P. Crutchfield</a></li> <li><a href="/wiki/Chris_Danforth" title="Chris Danforth">Chris Danforth</a></li> <li><a href="/wiki/Peter_Sheridan_Dodds" class="mw-redirect" title="Peter Sheridan Dodds">Peter Sheridan Dodds</a></li> <li><a href="/wiki/Brian_J._Enquist" title="Brian J. Enquist">Brian Enquist</a></li> <li><a href="/wiki/Joshua_M._Epstein" title="Joshua M. Epstein">Joshua Epstein</a></li> <li><a href="/wiki/J._Doyne_Farmer" title="J. Doyne Farmer">Doyne Farmer</a></li> <li><a href="/wiki/Jay_Forrester" class="mw-redirect" title="Jay Forrester">Jay Forrester</a></li> <li><a href="/wiki/Nigel_R._Franks" title="Nigel R. Franks">Nigel R. Franks</a></li> <li><a href="/wiki/Murray_Gell-Mann" title="Murray Gell-Mann">Murray Gell-Mann</a></li> <li><a href="/wiki/Carlos_Gershenson" title="Carlos Gershenson">Carlos Gershenson</a></li> <li><a href="/wiki/Nigel_Goldenfeld" title="Nigel Goldenfeld">Nigel Goldenfeld</a></li> <li><a href="/wiki/Vittorio_Guidano" title="Vittorio Guidano">Vittorio Guidano</a></li> <li><a href="/wiki/Hermann_Haken" title="Hermann Haken">Hermann Haken</a></li> <li><a href="/wiki/James_Hartle" title="James Hartle">James Hartle</a></li> <li><a href="/wiki/Friedrich_Hayek" title="Friedrich Hayek">F. A. Hayek</a></li> <li><a href="/wiki/Dirk_Helbing" title="Dirk Helbing">Dirk Helbing</a></li> <li><a href="/wiki/John_Henry_Holland" title="John Henry Holland">John Holland</a></li> <li><a href="/wiki/Alfred_H%C3%BCbler" title="Alfred Hübler">Alfred Hubler</a></li> <li><a href="/wiki/Arthur_Iberall" title="Arthur Iberall">Arthur Iberall</a></li> <li>Johannes Jaeger</li> <li><a href="/wiki/Stuart_Kauffman" title="Stuart Kauffman">Stuart Kauffman</a></li> <li><a href="/wiki/J._A._Scott_Kelso" title="J. A. Scott Kelso">J. A. Scott Kelso</a></li> <li><a href="/wiki/David_Krakauer_(scientist)" title="David Krakauer (scientist)">David Krakauer</a></li> <li><a href="/wiki/Simon_A._Levin" title="Simon A. Levin">Simon A. Levin</a></li> <li><a href="/wiki/Ellen_Levy" title="Ellen Levy">Ellen Levy</a></li> <li><a href="/wiki/Robert_May,_Baron_May_of_Oxford" title="Robert May, Baron May of Oxford">Robert May</a></li> <li><a href="/wiki/Donella_Meadows" title="Donella Meadows">Donella Meadows</a></li> <li><a href="/wiki/Jos%C3%A9_Fernando_Mendes" class="mw-redirect" title="José Fernando Mendes">José Fernando Mendes</a></li> <li><a href="/wiki/Melanie_Mitchell" title="Melanie Mitchell">Melanie Mitchell</a></li> <li><a href="/wiki/Cris_Moore" class="mw-redirect" title="Cris Moore">Cris Moore</a></li> <li><a href="/wiki/Yamir_Moreno" title="Yamir Moreno">Yamir Moreno</a></li> <li><a href="/wiki/Edgar_Morin" title="Edgar Morin">Edgar Morin</a></li> <li><a href="/wiki/Harold_J._Morowitz" title="Harold J. Morowitz">Harold Morowitz</a></li> <li><a href="/wiki/Adilson_E._Motter" title="Adilson E. Motter">Adilson E. Motter</a></li> <li><a href="/wiki/Scott_E._Page" title="Scott E. Page">Scott Page</a></li> <li><a href="/wiki/Luciano_Pietronero" title="Luciano Pietronero">Luciano Pietronero</a></li> <li><a href="/wiki/David_Pines" title="David Pines">David Pines</a></li> <li><a href="/wiki/Vladimir_Pokrovskii" title="Vladimir Pokrovskii">Vladimir Pokrovskii</a></li> <li><a href="/wiki/William_T._Powers" title="William T. Powers">William T. Powers</a></li> <li><a href="/wiki/Ilya_Prigogine" title="Ilya Prigogine">Ilya Prigogine</a></li> <li><a href="/wiki/Steen_Rasmussen_(physicist)" title="Steen Rasmussen (physicist)">Steen Rasmussen</a></li> <li><a href="/wiki/Sidney_Redner" title="Sidney Redner">Sidney Redner</a></li> <li><a href="/wiki/Jerry_Sabloff" title="Jerry Sabloff">Jerry Sabloff</a></li> <li><a href="/wiki/Cosma_Shalizi" title="Cosma Shalizi">Cosma Shalizi</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert Simon</a></li> <li><a href="/wiki/Dave_Snowden" title="Dave Snowden">Dave Snowden</a></li> <li><a href="/wiki/Sergei_Starostin" title="Sergei Starostin">Sergei Starostin</a></li> <li><a href="/wiki/Steven_Strogatz" title="Steven Strogatz">Steven Strogatz</a></li> <li><a href="/wiki/Stefan_Thurner" title="Stefan Thurner">Stefan Thurner</a></li> <li><a href="/wiki/Alessandro_Vespignani" title="Alessandro Vespignani">Alessandro Vespignani</a></li> <li><a href="/wiki/Andreas_Wagner" title="Andreas Wagner">Andreas Wagner</a></li> <li><a href="/wiki/Duncan_J._Watts" title="Duncan J. Watts">Duncan Watts</a></li> <li><a href="/wiki/Geoffrey_West" title="Geoffrey West">Geoffrey West</a></li> <li><a href="/wiki/Stephen_Wolfram" title="Stephen Wolfram">Stephen Wolfram</a></li> <li><a href="/wiki/David_Wolpert" title="David Wolpert">David Wolpert</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Complex-adaptive-system.jpg/48px-Complex-adaptive-system.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Complex-adaptive-system.jpg/64px-Complex-adaptive-system.jpg 2x" data-file-width="2100" data-file-height="1500" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Systems_science" title="Portal:Systems science">Systems science portal</a></span></li></ul> <table> <tbody><tr style="vertical-align:top"> <td style="padding-right:2em"> <ul><li><a href="/wiki/Biological_organisation" title="Biological organisation">Biological organisation</a></li> <li><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></li> <li><a href="/wiki/Cognitive_model#Dynamical_systems" title="Cognitive model">Cognitive modeling</a></li> <li><a href="/wiki/Cognitive_science" title="Cognitive science">Cognitive science</a></li> <li><a href="/wiki/Complex_(disambiguation)" class="mw-redirect mw-disambig" title="Complex (disambiguation)">Complex (disambiguation)</a></li> <li><a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">Complex adaptive system</a></li> <li><a href="/wiki/Complex_networks" class="mw-redirect" title="Complex networks">Complex networks</a></li> <li><a href="/wiki/Complexity" title="Complexity">Complexity</a></li> <li><a href="/wiki/Complexity_(disambiguation)" class="mw-disambig" title="Complexity (disambiguation)">Complexity (disambiguation)</a></li> <li><a href="/wiki/Complexity_economics" title="Complexity economics">Complexity economics</a></li> <li><a href="/wiki/Complexity_Science_Hub_Vienna" class="mw-redirect" title="Complexity Science Hub Vienna">Complexity Science Hub Vienna</a></li> <li><a href="/wiki/Cybernetics" title="Cybernetics">Cybernetics</a></li></ul> </td> <td style="padding-right:2em"> <ul><li><a href="/wiki/Decision_engineering" class="mw-redirect" title="Decision engineering">Decision engineering</a></li> <li><a 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href="/wiki/Systems_theory_in_anthropology" title="Systems theory in anthropology">Systems theory in anthropology</a></li> <li><a href="/wiki/Tektology" title="Tektology">Tektology</a></li> <li><a href="/wiki/Ultra-large-scale_systems" title="Ultra-large-scale systems">Ultra-large-scale systems</a></li> <li><a href="/wiki/VUCA" title="VUCA">Volatility, uncertainty, complexity and ambiguity</a></li></ul> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFLadymanLambertWiesner2013" class="citation journal cs1">Ladyman, James; Lambert, James; Wiesner, Karoline (2013). <a rel="nofollow" class="external text" href="https://philsci-archive.pitt.edu/9044/4/LLWultimate.pdf">"What is a complex system?"</a> <span class="cs1-format">(PDF)</span>. <i>European Journal for Philosophy of Science</i>. <b>3</b>: <span class="nowrap">33–</span>67. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs13194-012-0056-8">10.1007/s13194-012-0056-8</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 July</span> 2024</span>. <q>[S]pecial issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [...] [:] 6. 'A complex system is literally one in which there are multiple interactions between many different components.' (40, p. 105)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+for+Philosophy+of+Science&rft.atitle=What+is+a+complex+system%3F&rft.volume=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E33-%3C%2Fspan%3E67&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2Fs13194-012-0056-8&rft.aulast=Ladyman&rft.aufirst=James&rft.au=Lambert%2C+James&rft.au=Wiesner%2C+Karoline&rft_id=https%3A%2F%2Fphilsci-archive.pitt.edu%2F9044%2F4%2FLLWultimate.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLadymanLambertWiesner2013" class="citation journal cs1">Ladyman, James; Lambert, James; Wiesner, Karoline (2013). <a rel="nofollow" class="external text" href="https://philsci-archive.pitt.edu/9044/4/LLWultimate.pdf">"What is a complex system?"</a> <span class="cs1-format">(PDF)</span>. <i>European Journal for Philosophy of Science</i>. <b>3</b>: <span class="nowrap">33–</span>67. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs13194-012-0056-8">10.1007/s13194-012-0056-8</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 July</span> 2024</span>. <q>The following quotations (apart from the last one) come from a special issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [:] 8. 'In recent years the scientific community has coined the rubric 'complex system' to describe phenomena, structure, aggregates, organisms, or problems that share some common theme: (i) They are inherently complicated or intricate ...; (ii) they are rarely completely deterministic; (iii) mathematical models of the system are usually complex and involve non-linear, ill-posed, or chaotic behavior; (iv) the systems are predisposed to unexpected outcomes (so-called emergent behaviour).' (14, p. 410)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+for+Philosophy+of+Science&rft.atitle=What+is+a+complex+system%3F&rft.volume=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E33-%3C%2Fspan%3E67&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2Fs13194-012-0056-8&rft.aulast=Ladyman&rft.aufirst=James&rft.au=Lambert%2C+James&rft.au=Wiesner%2C+Karoline&rft_id=https%3A%2F%2Fphilsci-archive.pitt.edu%2F9044%2F4%2FLLWultimate.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Parker, B. R. (2013). <i>Chaos in the Cosmos: the Stunning Complexity of the Universe</i>. Springer.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Bekenstein, J. D. (2003). Information in the holographic universe, <i>Scientific American</i>, <i>289</i>(2), 58-65.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLadymanLambertWiesner2013" class="citation journal cs1">Ladyman, James; Lambert, James; Wiesner, Karoline (2013). <a rel="nofollow" class="external text" href="https://philsci-archive.pitt.edu/9044/4/LLWultimate.pdf">"What is a complex system?"</a> <span class="cs1-format">(PDF)</span>. <i>European Journal for Philosophy of Science</i>. <b>3</b>: <span class="nowrap">33–</span>67. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs13194-012-0056-8">10.1007/s13194-012-0056-8</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 July</span> 2024</span>. <q>The following quotations (apart from the last one) come from a special issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [...] [:] 3. 'In a general sense, the adjective 'complex' describes a system or component that by design or function or both is difficult to understand and verify. ...complexity is determined by such factors as the number of components and the intricacy of the interfaces between them, the number and intricacy of conditional branches, the degree of nesting, and the types of data structures.'(50, p. 92)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+for+Philosophy+of+Science&rft.atitle=What+is+a+complex+system%3F&rft.volume=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E33-%3C%2Fspan%3E67&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2Fs13194-012-0056-8&rft.aulast=Ladyman&rft.aufirst=James&rft.au=Lambert%2C+James&rft.au=Wiesner%2C+Karoline&rft_id=https%3A%2F%2Fphilsci-archive.pitt.edu%2F9044%2F4%2FLLWultimate.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLadymanLambertWiesner2013" class="citation journal cs1">Ladyman, James; Lambert, James; Wiesner, Karoline (2013). <a rel="nofollow" class="external text" href="https://philsci-archive.pitt.edu/9044/4/LLWultimate.pdf">"What is a complex system?"</a> <span class="cs1-format">(PDF)</span>. <i>European Journal for Philosophy of Science</i>. <b>3</b>: <span class="nowrap">33–</span>67. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs13194-012-0056-8">10.1007/s13194-012-0056-8</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 July</span> 2024</span>. <q>The following quotations (apart from the last one) come from a special issue of Science on 'Complex Systems' featuring many key figures in the field (Science 2 April 1999) [...] [:] 4. 'Complexity theory indicates that large populations of units can self-organize into aggregations that generate pattern, store information, and engage in collective decision-making.' (39, p. 99)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+for+Philosophy+of+Science&rft.atitle=What+is+a+complex+system%3F&rft.volume=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E33-%3C%2Fspan%3E67&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2Fs13194-012-0056-8&rft.aulast=Ladyman&rft.aufirst=James&rft.au=Lambert%2C+James&rft.au=Wiesner%2C+Karoline&rft_id=https%3A%2F%2Fphilsci-archive.pitt.edu%2F9044%2F4%2FLLWultimate.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBar-Yam2002" class="citation journal cs1">Bar-Yam, Yaneer (2002). <a rel="nofollow" class="external text" href="http://www.eolss.net/sample-chapters/c15/E1-29-01-00.pdf">"General Features of Complex Systems"</a> <span class="cs1-format">(PDF)</span>. <i>Encyclopedia of Life Support Systems</i>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.eolss.net/sample-chapters/c15/E1-29-01-00.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-10-09<span class="reference-accessdate">. Retrieved <span class="nowrap">16 September</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Encyclopedia+of+Life+Support+Systems&rft.atitle=General+Features+of+Complex+Systems&rft.date=2002&rft.aulast=Bar-Yam&rft.aufirst=Yaneer&rft_id=http%3A%2F%2Fwww.eolss.net%2Fsample-chapters%2Fc15%2FE1-29-01-00.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHolland2014" class="citation book cs1"><a href="/wiki/John_Henry_Holland" title="John Henry Holland">Holland, John H.</a> (2014). <i>Complexity: A Very Short Introduction</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-966254-8" title="Special:BookSources/978-0-19-966254-8"><bdi>978-0-19-966254-8</bdi></a>. <q>All CAS agents, whatever their particularities, have three levels of activity: <div class="paragraphbreak" style="margin-top:0.5em"></div> 1. Performance (moment-by-moment capabilities) <div class="paragraphbreak" style="margin-top:0.5em"></div> 2. Credit-assignment (rating the usefulness of available capabilities) <div class="paragraphbreak" style="margin-top:0.5em"></div> 3. Rule-discovery (generating new capabilities).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Complexity%3A+A+Very+Short+Introduction&rft.pub=Oxford+University+Press&rft.date=2014&rft.isbn=978-0-19-966254-8&rft.aulast=Holland&rft.aufirst=John+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSkrimizeaHaniotouParra2019" class="citation journal cs1">Skrimizea, Eirini; Haniotou, Helene; Parra, Constanza (2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F1473095218780515">"On the 'complexity turn' in planning: An adaptive rationale to navigate spaces and times of uncertainty"</a>. <i>Planning Theory</i>. <b>18</b>: <span class="nowrap">122–</span>142. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F1473095218780515">10.1177/1473095218780515</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:149578797">149578797</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Planning+Theory&rft.atitle=On+the+%27complexity+turn%27+in+planning%3A+An+adaptive+rationale+to+navigate+spaces+and+times+of+uncertainty&rft.volume=18&rft.pages=%3Cspan+class%3D%22nowrap%22%3E122-%3C%2Fspan%3E142&rft.date=2019&rft_id=info%3Adoi%2F10.1177%2F1473095218780515&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A149578797%23id-name%3DS2CID&rft.aulast=Skrimizea&rft.aufirst=Eirini&rft.au=Haniotou%2C+Helene&rft.au=Parra%2C+Constanza&rft_id=https%3A%2F%2Fdoi.org%2F10.1177%252F1473095218780515&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlan_Randall2011" class="citation book cs1"><a href="/w/index.php?title=Alan_Randall_(economist)&action=edit&redlink=1" class="new" title="Alan Randall (economist) (page does not exist)">Alan Randall</a> (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=IlHj3fvJzMsC"><i>Risk and Precaution</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781139494793" title="Special:BookSources/9781139494793"><bdi>9781139494793</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Risk+and+Precaution&rft.pub=Cambridge+University+Press&rft.date=2011&rft.isbn=9781139494793&rft.au=Alan+Randall&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DIlHj3fvJzMsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPokrovskii2021" class="citation book cs1">Pokrovskii, Vladimir (2021). <i>Thermodynamics of Complex Systems: Principles and applications</i>. 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Jelle; Leemput, Ingrid A.; Weinans, Els; Quax, Rick; Dakos, Vasilis; Nes, Egbert H.; Bascompte, Jordi; Scheffer, Marten (2020). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6916369">"Foreseeing the future of mutualistic communities beyond collapse"</a>. <i>Ecology Letters</i>. <b>23</b> (1): <span class="nowrap">2–</span>15. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020EcolL..23....2L">2020EcolL..23....2L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fele.13401">10.1111/ele.13401</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6916369">6916369</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/31707763">31707763</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ecology+Letters&rft.atitle=Foreseeing+the+future+of+mutualistic+communities+beyond+collapse&rft.volume=23&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2-%3C%2Fspan%3E15&rft.date=2020&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6916369%23id-name%3DPMC&rft_id=info%3Apmid%2F31707763&rft_id=info%3Adoi%2F10.1111%2Fele.13401&rft_id=info%3Abibcode%2F2020EcolL..23....2L&rft.aulast=Lever&rft.aufirst=J.+Jelle&rft.au=Leemput%2C+Ingrid+A.&rft.au=Weinans%2C+Els&rft.au=Quax%2C+Rick&rft.au=Dakos%2C+Vasilis&rft.au=Nes%2C+Egbert+H.&rft.au=Bascompte%2C+Jordi&rft.au=Scheffer%2C+Marten&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6916369&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchefferCarpenterFoleyFolke2001" class="citation journal cs1">Scheffer, Marten; Carpenter, Steve; Foley, Jonathan A.; Folke, Carl; Walker, Brian (October 2001). <a rel="nofollow" class="external text" href="https://www.nature.com/articles/35098000">"Catastrophic shifts in ecosystems"</a>. <i>Nature</i>. <b>413</b> (6856): <span class="nowrap">591–</span>596. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001Natur.413..591S">2001Natur.413..591S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F35098000">10.1038/35098000</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1476-4687">1476-4687</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11595939">11595939</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:8001853">8001853</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Catastrophic+shifts+in+ecosystems&rft.volume=413&rft.issue=6856&rft.pages=%3Cspan+class%3D%22nowrap%22%3E591-%3C%2Fspan%3E596&rft.date=2001-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A8001853%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2001Natur.413..591S&rft.issn=1476-4687&rft_id=info%3Adoi%2F10.1038%2F35098000&rft_id=info%3Apmid%2F11595939&rft.aulast=Scheffer&rft.aufirst=Marten&rft.au=Carpenter%2C+Steve&rft.au=Foley%2C+Jonathan+A.&rft.au=Folke%2C+Carl&rft.au=Walker%2C+Brian&rft_id=https%3A%2F%2Fwww.nature.com%2Farticles%2F35098000&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScheffer2009" class="citation book cs1">Scheffer, Marten (26 July 2009). <i>Critical transitions in nature and society</i>. 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(2004). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC374315">"The architecture of complex weighted networks"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>101</b> (11): <span class="nowrap">3747–</span>3752. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/0311416">cond-mat/0311416</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004PNAS..101.3747B">2004PNAS..101.3747B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.0400087101">10.1073/pnas.0400087101</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0027-8424">0027-8424</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC374315">374315</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15007165">15007165</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences&rft.atitle=The+architecture+of+complex+weighted+networks&rft.volume=101&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3747-%3C%2Fspan%3E3752&rft.date=2004&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC374315%23id-name%3DPMC&rft_id=info%3Abibcode%2F2004PNAS..101.3747B&rft_id=info%3Aarxiv%2Fcond-mat%2F0311416&rft.issn=0027-8424&rft_id=info%3Adoi%2F10.1073%2Fpnas.0400087101&rft_id=info%3Apmid%2F15007165&rft.aulast=Barrat&rft.aufirst=A.&rft.au=Barthelemy%2C+M.&rft.au=Pastor-Satorras%2C+R.&rft.au=Vespignani%2C+A.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC374315&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=17" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200424112123/https://complexityexplained.github.io/">Complexity Explained</a>.</li> <li><a href="/wiki/Luis_Amaral" class="mw-redirect" title="Luis Amaral">L.A.N. Amaral</a> and J.M. Ottino, <a rel="nofollow" class="external text" href="http://amaral-lab.org/media/publication_pdfs/Amaral-2004-Eur.Phys.J.B-38-147.pdf"><i>Complex networks – augmenting the framework for the study of complex system</i></a>, 2004.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChuStrandFjelland2003" class="citation journal cs1">Chu, D.; Strand, R.; Fjelland, R. (2003). "Theories of complexity". <i>Complexity</i>. <b>8</b> (3): <span class="nowrap">19–</span>30. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003Cmplx...8c..19C">2003Cmplx...8c..19C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcplx.10059">10.1002/cplx.10059</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Complexity&rft.atitle=Theories+of+complexity&rft.volume=8&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E19-%3C%2Fspan%3E30&rft.date=2003&rft_id=info%3Adoi%2F10.1002%2Fcplx.10059&rft_id=info%3Abibcode%2F2003Cmplx...8c..19C&rft.aulast=Chu&rft.aufirst=D.&rft.au=Strand%2C+R.&rft.au=Fjelland%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></li> <li><a href="/wiki/Walter_Clemens,_Jr." class="mw-redirect" title="Walter Clemens, Jr.">Walter Clemens, Jr.</a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150219221633/http://www.sunypress.edu/p-5782-complexity-science-and-world-af.aspx"><i>Complexity Science and World Affairs</i></a>, SUNY Press, 2013.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGell-Mann1995" class="citation journal cs1">Gell-Mann, Murray (1995). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcplx.6130010502">"Let's Call It Plectics"</a>. <i>Complexity</i>. <b>1</b> (5): <span class="nowrap">3–</span>5. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996Cmplx...1e...3G">1996Cmplx...1e...3G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcplx.6130010502">10.1002/cplx.6130010502</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Complexity&rft.atitle=Let%27s+Call+It+Plectics&rft.volume=1&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3-%3C%2Fspan%3E5&rft.date=1995&rft_id=info%3Adoi%2F10.1002%2Fcplx.6130010502&rft_id=info%3Abibcode%2F1996Cmplx...1e...3G&rft.aulast=Gell-Mann&rft.aufirst=Murray&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fcplx.6130010502&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></li> <li>A. Gogolin, A. Nersesyan and A. Tsvelik, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070715195144/http://www.cmth.bnl.gov/~tsvelik/theory.html"><i>Theory of strongly correlated systems </i></a>, Cambridge University Press, 1999.</li> <li><a href="/wiki/Nigel_Goldenfeld" title="Nigel Goldenfeld">Nigel Goldenfeld</a> and Leo P. Kadanoff, <a rel="nofollow" class="external text" href="http://guava.physics.uiuc.edu/~nigel/articles/complexity.html"><i>Simple Lessons from Complexity</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170928102108/http://guava.physics.uiuc.edu/~nigel/articles/complexity.html">Archived</a> 2017-09-28 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, 1999</li> <li>Kelly, K. (1995). <a rel="nofollow" class="external text" href="http://www.kk.org/outofcontrol/contents.php"><i>Out of Control</i></a>, Perseus Books Group.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOrlandoPisarchickStoop2021" class="citation book cs1">Orlando, Giuseppe Orlando; Pisarchick, Alexander; Stoop, Ruedi (2021). <a rel="nofollow" class="external text" href="https://link.springer.com/book/10.1007/978-3-030-70982-2#editorsandaffiliations"><i>Nonlinearities in Economics</i></a>. Dynamic Modeling and Econometrics in Economics and Finance. Vol. 29. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-70982-2">10.1007/978-3-030-70982-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-030-70981-5" title="Special:BookSources/978-3-030-70981-5"><bdi>978-3-030-70981-5</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:239756912">239756912</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nonlinearities+in+Economics&rft.series=Dynamic+Modeling+and+Econometrics+in+Economics+and+Finance&rft.date=2021&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A239756912%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-3-030-70982-2&rft.isbn=978-3-030-70981-5&rft.aulast=Orlando&rft.aufirst=Giuseppe+Orlando&rft.au=Pisarchick%2C+Alexander&rft.au=Stoop%2C+Ruedi&rft_id=https%3A%2F%2Flink.springer.com%2Fbook%2F10.1007%2F978-3-030-70982-2%23editorsandaffiliations&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></li> <li>Syed M. Mehmud (2011), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120426052819/http://predictivemodeler.com/sitecontent/book/Ch06_Applications/Actuarial/HEC_Model/Healthcare%20Exchange%20Complexity%20Model%20-%20Report%20-%20Aug2011.pdf"><i>A Healthcare Exchange Complexity Model</i></a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110220054920/http://www.oeaw.ac.at/byzanz/repository/Preiser_WorkingPapers_Calculating_I.pdf">Preiser-Kapeller, Johannes, "Calculating Byzantium. Social Network Analysis and Complexity Sciences as tools for the exploration of medieval social dynamics". August 2010</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDonald_Snooks2008" class="citation journal cs1">Donald Snooks, Graeme (2008). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcplx.20225">"A general theory of complex living systems: Exploring the demand side of dynamics"</a>. <i>Complexity</i>. <b>13</b> (6): <span class="nowrap">12–</span>20. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008Cmplx..13f..12S">2008Cmplx..13f..12S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcplx.20225">10.1002/cplx.20225</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Complexity&rft.atitle=A+general+theory+of+complex+living+systems%3A+Exploring+the+demand+side+of+dynamics&rft.volume=13&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E12-%3C%2Fspan%3E20&rft.date=2008&rft_id=info%3Adoi%2F10.1002%2Fcplx.20225&rft_id=info%3Abibcode%2F2008Cmplx..13f..12S&rft.aulast=Donald+Snooks&rft.aufirst=Graeme&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fcplx.20225&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComplex+system" class="Z3988"></span></li> <li><a href="/wiki/Stefan_Thurner" title="Stefan Thurner">Stefan Thurner</a>, Peter Klimek, Rudolf Hanel: <i>Introduction to the Theory of Complex Systems</i>, Oxford University Press, 2018, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0198821939" title="Special:BookSources/978-0198821939">978-0198821939</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200728201713/https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/publication/2016/10/31/Bulletin_Fall_2014_FINAL.pdf">SFI @30, Foundations & Frontiers</a> (2014).</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complex_system&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; 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navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Complex_systems_topics" title="Template:Complex systems topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Complex_systems_topics" title="Template talk:Complex systems topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Complex_systems_topics" title="Special:EditPage/Template:Complex systems topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Complex_systems216" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Complex systems</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Emergence" title="Emergence">Emergence</a></li> <li><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Collective_behavior" title="Collective behavior">Collective <br />behavior</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Social_dynamics" title="Social dynamics">Social dynamics</a></li> <li><a href="/wiki/Collective_intelligence" title="Collective intelligence">Collective intelligence</a></li> <li><a href="/wiki/Collective_action" title="Collective action">Collective action</a></li> <li><a href="/wiki/Collective_consciousness" title="Collective consciousness">Collective consciousness</a></li> <li><a href="/wiki/Self-organized_criticality" title="Self-organized criticality">Self-organized criticality</a></li> <li><a href="/wiki/Herd_mentality" title="Herd mentality">Herd mentality</a></li> <li><a href="/wiki/Phase_transition" title="Phase transition">Phase transition</a></li> <li><a href="/wiki/Agent-based_modelling" class="mw-redirect" title="Agent-based modelling">Agent-based modelling</a></li> <li><a href="/wiki/Synchronization" title="Synchronization">Synchronization</a></li> <li><a href="/wiki/Ant_colony_optimization" class="mw-redirect" title="Ant colony optimization">Ant colony optimization</a></li> <li><a href="/wiki/Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a></li> <li><a href="/wiki/Swarm_behaviour" title="Swarm behaviour">Swarm behaviour</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Evolution" title="Evolution">Evolution</a> and <br /><a href="/wiki/Adaptation" title="Adaptation">adaptation</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural network</a></li> <li><a href="/wiki/Evolutionary_computation" title="Evolutionary computation">Evolutionary computation</a></li> <li><a href="/wiki/Genetic_algorithms" class="mw-redirect" title="Genetic algorithms">Genetic algorithms</a></li> <li><a href="/wiki/Genetic_programming" title="Genetic programming">Genetic programming</a></li> <li><a href="/wiki/Artificial_life" title="Artificial life">Artificial life</a></li> <li><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a></li> <li><a href="/wiki/Evolutionary_developmental_biology" title="Evolutionary developmental biology">Evolutionary developmental biology</a></li> <li><a href="/wiki/Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</a></li> <li><a href="/wiki/Evolutionary_robotics" title="Evolutionary robotics">Evolutionary robotics</a></li> <li><a href="/wiki/Evolvability" title="Evolvability">Evolvability</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Game_theory" title="Game theory">Game theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">Prisoner's dilemma</a></li> <li><a href="/wiki/Rational_choice_theory" class="mw-redirect" title="Rational choice theory">Rational choice theory</a></li> <li><a href="/wiki/Bounded_rationality" title="Bounded rationality">Bounded rationality</a></li> <li><a href="/wiki/Evolutionary_game_theory" title="Evolutionary 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title="Systems biology">Systems biology</a></li> <li><a href="/wiki/Dynamic_network_analysis" title="Dynamic network analysis">Dynamic networks</a></li> <li><a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">Adaptive networks</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Nonlinear_dynamics" class="mw-redirect" title="Nonlinear dynamics">Nonlinear dynamics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Time_series_analysis" class="mw-redirect" title="Time series analysis">Time series analysis</a></li> <li><a href="/wiki/Ordinary_differential_equations" class="mw-redirect" title="Ordinary differential equations">Ordinary differential equations</a></li> <li><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li> <li><a href="/wiki/Attractor" title="Attractor">Attractor</a></li> <li><a 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