Document Zbl 1096.92001

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Cybern.</a> <a href="/?q=in%3A113047" title="Articles in this Issue">92, No. 1, 38-53 (2005)</a>. </div> <div class="abstract">Summary: We describe a simple yet general method to analyze networks of coupled identical nonlinear oscillators and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized) results on synchronization, antisynchronization, and oscillator death. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positive definite diffusion coupling, it can be shown that synchronization always occurs globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when the network structure varies abruptly and asynchronously, as in “flocks” of oscillators or dynamic elements.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5048817">Cited in <strong>77</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A92B05" title="MSC2020">92B05</a> </td> <td class="space"> General biology and biomathematics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37N25" title="MSC2020">37N25</a> </td> <td class="space"> Dynamical systems in biology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A99" title="MSC2020">15A99</a> </td> <td class="space"> Basic linear algebra </td> </tr></table> </div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1096.92001" data-ciurl="/ci/05048817" data-biburl="/bibtex/05048817.bib" data-amsurl="/amsrefs/05048817.bib" data-xmlurl="/xml/05048817.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05048817.pdf" title="Zbl 1096.92001 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s00422-004-0527-x" aria-label="DOI for “On partial contraction analysis for coupled nonlinear oscillators”" title="10.1007/s00422-004-0527-x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aronson DG, Ermentrout GB, Kopell N (1990) Amplitude response of coupled oscillators. 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