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<!DOCTYPE html> <html lang="en" class="no-js"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="robots" content="max-image-preview:large"> <meta name="access" content="No"> <meta name="360-site-verification" content="1268d79b5e96aecf3ff2a7dac04ad990" /> <title>Multistability Analysis of a Fractional-Order Multi-Wing Chaotic System and its Circuit Realization | Mobile Networks and Applications</title> <meta name="twitter:site" content="@SpringerLink"/> <meta name="twitter:card" content="summary_large_image"/> <meta name="twitter:image:alt" content="Content cover image"/> <meta name="twitter:title" content="Multistability Analysis of a Fractional-Order Multi-Wing Chaotic System and its Circuit Realization"/> <meta name="twitter:description" content="Mobile Networks and Applications - The multi-scroll or multi-wing attractor generated by the chaotic system has a complicated structure. Based on the definition of conformal fractional-order, the..."/> <meta name="twitter:image" content="https://static-content.springer.com/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig1_HTML.png"/> <meta name="journal_id" content="11036"/> <meta name="dc.title" content="Multistability Analysis of a Fractional-Order Multi-Wing Chaotic System and its Circuit Realization"/> <meta name="dc.source" content="Mobile Networks and Applications 2024"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Springer"/> <meta name="dc.date" content="2024-11-15"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2024 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature"/> <meta name="dc.rights" content="2024 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="The multi-scroll or multi-wing attractor generated by the chaotic system has a complicated structure. Based on the definition of conformal fractional-order, the Adomian decomposition method is used to solve the fractional-order multi-wing chaotic system. It is worth noting that this system has been found to have at least six multi-wing chaotic attractors with different shapes. The system parameters are used as bifurcation control parameters, and multiple bifurcation behaviors and multi-wing attractors can be observed. The results show that the 0.9-order chaotic system still has multiple stable phenomena, and some typical coexistence phenomena such as period and period, period and chaos, and chaos and chaos can all be found. Finally, an analog circuit was built on the Multisim simulation software, and the chaotic system successfully carry out on the DSP board. This research gives guidance on applying the conformable fractional-order theory to nonlinear systems."/> <meta name="prism.issn" content="1572-8153"/> <meta name="prism.publicationName" content="Mobile Networks and Applications"/> <meta name="prism.publicationDate" content="2024-11-15"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="11"/> <meta name="prism.copyright" content="2024 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://link.springer.com/article/10.1007/s11036-023-02155-1"/> <meta name="prism.doi" content="doi:10.1007/s11036-023-02155-1"/> <meta name="citation_pdf_url" content="https://link.springer.com/content/pdf/10.1007/s11036-023-02155-1.pdf"/> <meta name="citation_fulltext_html_url" content="https://link.springer.com/article/10.1007/s11036-023-02155-1"/> <meta name="citation_journal_title" content="Mobile Networks and Applications"/> <meta name="citation_journal_abbrev" content="Mobile Netw Appl"/> <meta name="citation_publisher" content="Springer US"/> <meta name="citation_issn" content="1572-8153"/> <meta name="citation_title" content="Multistability Analysis of a Fractional-Order Multi-Wing Chaotic System and its Circuit Realization"/> <meta name="citation_online_date" content="2024/11/15"/> <meta name="citation_firstpage" content="1"/> <meta name="citation_lastpage" content="11"/> <meta name="citation_article_type" content="Article"/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1007/s11036-023-02155-1"/> <meta name="DOI" content="10.1007/s11036-023-02155-1"/> <meta name="size" content="270720"/> <meta name="citation_doi" content="10.1007/s11036-023-02155-1"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1007/s11036-023-02155-1&api_key="/> <meta name="description" content="The multi-scroll or multi-wing attractor generated by the chaotic system has a complicated structure. Based on the definition of conformal fractional-order"/> <meta name="dc.creator" content="Liu, Tianming"/> <meta name="dc.creator" content="Sun, Bo"/> <meta name="dc.creator" content="Li, Peng"/> <meta name="dc.creator" content="Ma, Tao"/> <meta name="dc.creator" content="Ma, Yanjie"/> <meta name="dc.subject" content="Communications Engineering, Networks"/> <meta name="dc.subject" content="Computer Communication Networks"/> <meta name="dc.subject" content="Electrical Engineering"/> <meta name="dc.subject" content="IT in Business"/> <meta name="citation_reference" content="citation_journal_title=J Appl Anal Comput; citation_title=Bifurcations and synchronization of the fractional-order simplified lorenz hyperchaotic system; citation_author=W Yan, S He, H Wang, K Sun; citation_volume=5; citation_issue=2; citation_publication_date=2015; citation_pages=210-219; citation_id=CR1"/> <meta name="citation_reference" content="citation_journal_title=Mathematics; citation_title=Fractional calculus: Integral and differential equations of fractional order; citation_author=R Gorenflo, F Mainardi; citation_volume=49; citation_issue=2; citation_publication_date=2008; citation_pages=277-290; citation_id=CR2"/> <meta name="citation_reference" content="citation_journal_title=Commun Nonlinear Sci Numer Simul; citation_title=Recent history of fractional calculus; citation_author=JT Machado, V Kiryakova, F Mainardi; citation_volume=16; citation_issue=3; citation_publication_date=2011; citation_pages=1140-1153; citation_doi=10.1016/j.cnsns.2010.05.027; citation_id=CR3"/> <meta name="citation_reference" content="citation_journal_title=IEEE Trans Ind Inform; citation_title=Reinforcement learning-based multislot double-threshold spectrum sensing with bayesian fusion for industrial big spectrum data; citation_author=X Liu, C Sun, M Zhou, C Wu, B Peng, P Li; citation_volume=17; citation_issue=5; citation_publication_date=2021; citation_pages=3391-3400; citation_doi=10.1109/TII.2020.2987421; citation_id=CR4"/> <meta name="citation_reference" content="Liu X, Sun C, Yau K-LA, Wu C (2022) Joint collaborative big spectrum data sensing and reinforcement learning based dynamic spectrum access for cognitive internet of vehicles. IEEE Trans Intell Transp Syst 1–11. https://doi.org/10.1109/TITS.2022.3175570 "/> <meta name="citation_reference" content="citation_journal_title=IEEE Internet Things J; citation_title=Uplink resource allocation for noma-based hybrid spectrum access in 6g-enabled cognitive internet of things; citation_author=X Liu, H Ding, S Hu; citation_volume=8; citation_issue=20; citation_publication_date=2021; citation_pages=15049-15058; citation_doi=10.1109/JIOT.2020.3007017; citation_id=CR6"/> <meta name="citation_reference" content="citation_journal_title=Chaos; citation_title=A new chaotic oscillator with free control; citation_author=C Li, JC Sprott, A Akgul, HHC Iu, Y Zhao; citation_volume=27; citation_issue=8; citation_publication_date=2017; citation_doi=10.1063/1.4997051; citation_id=CR7"/> <meta name="citation_reference" content="citation_journal_title=Rep Math Phys; citation_title=Nonlocal phenomena in quantum mechanics with fractional calculus; citation_author=KG Atman, H Şirin; citation_volume=86; citation_issue=2; citation_publication_date=2020; citation_pages=263-270; citation_doi=10.1016/S0034-4877(20)30075-6; citation_id=CR8"/> <meta name="citation_reference" content="citation_journal_title=IEEE Trans Ind Informa; citation_title=Reinforcement-learning-based dynamic spectrum access for software-defined cognitive industrial internet of things; citation_author=X Liu, C Sun, W Yu, M Zhou; citation_volume=18; citation_issue=6; citation_publication_date=2022; citation_pages=4244-4253; citation_doi=10.1109/TII.2021.3113949; citation_id=CR9"/> <meta name="citation_reference" content="citation_journal_title=Int J Math Math Sci; citation_title=Recent applications of fractional calculus to science and engineering; citation_author=D Lokenath; citation_volume=2003; citation_issue=54; citation_publication_date=2014; citation_pages=3413-3442; citation_id=CR10"/> <meta name="citation_reference" content="citation_journal_title=Int J Adapt Control Signal Process; citation_title=Control and synchronization of fractional-order chaotic satellite systems using feedback and adaptive control techniques; citation_author=S Kumar, AE Matouk, H Chaudhary, S Kant; citation_volume=35; citation_issue=4; citation_publication_date=2021; citation_pages=484-497; citation_doi=10.1002/acs.3207; citation_id=CR11"/> <meta name="citation_reference" content="citation_journal_title=IEEE Wirel Commun; citation_title=Big-data-based intelligent spectrum sensing for heterogeneous spectrum communications in 5g; citation_author=X Liu, Q Sun, W Lu, C Wu, H Ding; citation_volume=27; citation_issue=5; citation_publication_date=2020; citation_pages=67-73; citation_doi=10.1109/MWC.001.1900493; citation_id=CR12"/> <meta name="citation_reference" content="citation_journal_title=Polym Adv Technol; citation_title=Predictive model for stress relaxation behavior of glassy polymers based on variable-order fractional calculus; citation_author=G Xiang, D Yin, R Meng, C Cao; citation_volume=32; citation_issue=2; citation_publication_date=2021; citation_pages=703-713; citation_doi=10.1002/pat.5123; citation_id=CR13"/> <meta name="citation_reference" content="citation_journal_title=IEEE Trans Circ Syst I Regular Pap; citation_title=Neural bursting and synchronization emulated by neural networks and circuits; citation_author=H Lin, C Wang, C Chen, Y Sun, C Zhou, C Xu, Q Hong; citation_volume=68; citation_issue=8; citation_publication_date=2021; citation_pages=3397-3410; citation_doi=10.1109/TCSI.2021.3081150; citation_id=CR14"/> <meta name="citation_reference" content="citation_journal_title=J Comput Appl Math; citation_title=A new definition of fractional derivative; citation_author=R Khalil, M Al Horani, A Yousef, M Sababheh; citation_volume=264; citation_publication_date=2014; citation_pages=65-70; citation_doi=10.1016/j.cam.2014.01.002; citation_id=CR15"/> <meta name="citation_reference" content="citation_journal_title=J Comput Appl Math; citation_title=On conformable fractional calculus; citation_author=T Abdeljawad; citation_volume=279; citation_publication_date=2015; citation_pages=57-66; citation_doi=10.1016/j.cam.2014.10.016; citation_id=CR16"/> <meta name="citation_reference" content="Wang Y (2018) Dynamic analysis and synchronization of conformable fractional-order chaotic systems. Eur Phys J Plus 133(11)"/> <meta name="citation_reference" content="citation_journal_title=Calcolo; citation_title=General conformable fractional derivative and its physical interpretation; citation_author=D Zhao, M Luo; citation_volume=54; citation_issue=3; citation_publication_date=2017; citation_pages=903-917; citation_doi=10.1007/s10092-017-0213-8; citation_id=CR18"/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Plus; citation_title=Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative; citation_author=S He, K Sun, X Mei, B Yan, S Xu; citation_volume=132; citation_issue=1; citation_publication_date=2017; citation_pages=36; citation_doi=10.1140/epjp/i2017-11306-3; citation_id=CR19"/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Plus; citation_title=Fractional-order simplest memristor-based chaotic circuit with new derivative; citation_author=J Ruan, K Sun, J Mou, S He, L Zhang; citation_volume=133; citation_issue=1; citation_publication_date=2018; citation_pages=3; citation_doi=10.1140/epjp/i2018-11828-0; citation_id=CR20"/> <meta name="citation_reference" content="citation_journal_title=Optics Lasers Eng; citation_title=A one-time pad color image cryptosystem based on sha-3 and multiple chaotic systems; citation_author=X Wang, S Wang, Y Zhang, C Luo; citation_volume=103; citation_publication_date=2018; citation_pages=1-8; citation_doi=10.1016/j.optlaseng.2017.11.009; citation_id=CR21"/> <meta name="citation_reference" content="citation_journal_title=Int J Bifurcation Chaos; citation_title=An optical image encryption algorithm based on a fractional-order laser hyperchaotic system; citation_author=X Li, J Mou, Y Cao, S Banerjee; citation_volume=32; citation_issue=03; citation_publication_date=2022; citation_pages=2250035; citation_doi=10.1142/S0218127422500353; citation_id=CR22"/> <meta name="citation_reference" content="citation_journal_title=Chin Phys B; citation_title=Design and multistability analysis of five-value memristor based chaotic system with hidden attractors; citation_author=LL Huang, S Liu, JH Xiang, YuL Wang; citation_volume=30; citation_issue=10; citation_publication_date=2021; citation_pages=100506-100506; citation_doi=10.1088/1674-1056/ac1e13; citation_id=CR23"/> <meta name="citation_reference" content="citation_journal_title=Chaos; citation_title=Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse; citation_author=Z Tabekoueng Njitacke, I Sami Doubla, J Kengne, A Cheukem; citation_volume=30; citation_issue=2; citation_publication_date=2020; citation_doi=10.1063/1.5132280; citation_id=CR24"/> <meta name="citation_reference" content="(2022) An effective multiple-image encryption algorithm based on 3d cube and hyperchaotic map. J King Saud University Comput Inf Sci 34(4):1535–1551. https://doi.org/10.1016/j.jksuci.2022.01.017 "/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Spec Top; citation_title=Cosine chaotification technique to enhance chaos and complexity of discrete systems; citation_author=H Natiq, S Banerjee, MRM Said; citation_volume=228; citation_issue=1; citation_publication_date=2019; citation_pages=185-194; citation_doi=10.1140/epjst/e2019-800206-9; citation_id=CR26"/> <meta name="citation_reference" content="citation_journal_title=Chaos, Solitons Fractals; citation_title=Design and dsp implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption; citation_author=X Li, J Mou, S Banerjee, Z Wang, Y Cao; citation_volume=159; citation_publication_date=2022; citation_doi=10.1016/j.chaos.2022.112133; citation_id=CR27"/> <meta name="citation_reference" content="Lai Q, Kuate P, Liu F, Iu HC (2019) An extremely simple chaotic system with infinitely many coexisting attractors. Circ Syst II Express Briefs IEEE Trans PP(99):1–1. https://doi.org/10.1109/TCSII.2019.2927371 "/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Spec Top; citation_title=Self-reproducing dynamics in a two-dimensional discrete map; citation_author=C Li, Z Chen, X Yang, S He, Y Yang, J Du; citation_volume=230; citation_issue=7; citation_publication_date=2021; citation_pages=1959-1970; citation_doi=10.1140/epjs/s11734-021-00182-1; citation_id=CR29"/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Spec Top; citation_title=A hyperchaotic map with multi-elliptic cavities based on modulation and coupling; citation_author=C Wu, K Sun, Y Xiao; citation_volume=230; citation_issue=7; citation_publication_date=2021; citation_pages=2011-2020; citation_doi=10.1140/epjs/s11734-021-00126-9; citation_id=CR30"/> <meta name="citation_reference" content="citation_journal_title=Nonlinear Dyn; citation_title=A s-type bistable locally active memristor model and its analog implementation in an oscillator circuit; citation_author=C Li, H Li, W Xie, J Du; citation_volume=106; citation_issue=1; citation_publication_date=2021; citation_pages=1041-1058; citation_doi=10.1007/s11071-021-06814-4; citation_id=CR31"/> <meta name="citation_reference" content="citation_journal_title=Nonlinear Dyn; citation_title=Image encryption algorithm with circle index table scrambling and partition diffusion; citation_author=Y Zhou, C Li, W Li, H Li, W Feng, K Qian; citation_volume=103; citation_issue=2; citation_publication_date=2021; citation_pages=2043-2061; citation_doi=10.1007/s11071-021-06206-8; citation_id=CR32"/> <meta name="citation_reference" content="citation_journal_title=Nonlinear Dyn; citation_title=A fast and efficient multiple images encryption based on single-channel encryption and chaotic system; citation_author=X Gao, J Mou, L Xiong, Y Sha, H Yan, Y Cao; citation_volume=108; citation_publication_date=2022; citation_pages=613-636; citation_doi=10.1007/s11071-021-07192-7; citation_id=CR33"/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Plus; citation_title=A new set of hyperchaotic maps based on modulation and coupling; citation_author=X Han, J Mou, H Jahanshahi, Y Cao, F Bu; citation_volume=137; citation_issue=4; citation_publication_date=2022; citation_pages=523; citation_doi=10.1140/epjp/s13360-022-02734-3; citation_id=CR34"/> <meta name="citation_reference" content="citation_journal_title=Eur Phys J Spec Top; citation_title=A hyperchaotic map with multi-elliptic cavities based on modulation and coupling; citation_author=C Wu, K Sun, Y Xiao; citation_volume=230; citation_issue=7; citation_publication_date=2021; citation_pages=2011-2020; citation_doi=10.1140/epjs/s11734-021-00126-9; citation_id=CR35"/> <meta name="citation_reference" content="citation_journal_title=Chin J Phys; citation_title=One to four-wing chaotic attractors coined from a novel 3d fractional-order chaotic system with complex dynamics; citation_author=S Zhang, Y Zeng, Z Li; citation_volume=56; citation_issue=3; citation_publication_date=2018; citation_pages=793-806; citation_doi=10.1016/j.cjph.2018.03.002; citation_id=CR36"/> <meta name="citation_reference" content="citation_journal_title=Multimedia Tools Appl; citation_title=Image encryption scheme with bit-level scrambling and multiplication diffusion; citation_author=C-L Li, Y Zhou, H-M Li, W Feng, J-R Du; citation_volume=80; citation_issue=12; citation_publication_date=2021; citation_pages=18479-18501; citation_doi=10.1007/s11042-021-10631-7; citation_id=CR37"/> <meta name="citation_reference" content="citation_journal_title=Int J Bifurcation Chaos; citation_title=Dynamics of a new multi-cavity hyperchaotic map and its dsp implementation; citation_author=Y Xiao, K Sun, M Yu, X Xu; citation_volume=29; citation_issue=14; citation_publication_date=2019; citation_pages=1950194; citation_doi=10.1142/S0218127419501943; citation_id=CR38"/> <meta name="citation_reference" content="citation_journal_title=Int J Bifurcation Chaos; citation_title=A novel nonideal flux-controlled memristor model for generating arbitrary multidouble-scroll and multi-double-wing attractors; citation_author=S Zhang, J Zheng, X Wang, Z Zeng, X Peng; citation_volume=31; citation_issue=06; citation_publication_date=2021; citation_pages=2150086; citation_doi=10.1142/S0218127421500863; citation_id=CR39"/> <meta name="citation_reference" content="Gao X, Mou J, Banerjee S, Cao Y, Xiong L, Chen X (2022) An effective multiple-image encryption algorithm based on 3d cube and hyperchaotic map. J King Saud University Comput Inf Sci 34(4):1535–1551. https://doi.org/10.1016/j.jksuci.2022.01.017 "/> <meta name="citation_reference" content="citation_journal_title=Chaos Interdiscip J Nonlinear Sci; citation_title=A novel non-equilibrium memristorbased system with multi-wing attractors and multiple transient transitions; citation_author=S Gu, Q Peng, X Leng, B Du; citation_volume=31; citation_issue=3; citation_publication_date=2021; citation_doi=10.1063/5.0039121; citation_id=CR41"/> <meta name="citation_reference" content="citation_journal_title=Complexity; citation_title=Three-dimensional memristive hindmarsh-rose neuron model with hidden coexisting asymmetric behaviors; citation_author=B Bao, A Hu, H Bao, Q Xu, H Wu; citation_volume=4; citation_publication_date=2018; citation_pages=1-11; citation_doi=10.1155/2018/3872573; citation_id=CR42"/> <meta name="citation_reference" content="Xiong L, Zhang X, Sufen T, Qi L, Zhang P (2020) Experimental verification of a comparative research platform for various nonlinearity and weak signal detection based on a memristor-based chua’s system. Int J Bifurcation Chaos 30(13)"/> <meta name="citation_reference" content="Jia HY, Chen ZQ, Wei X (2013) Analysis and circuit implementation for the fractional-order lorenz system. Acta Physica Sinica –Chinese Edition–62(14):140503–113"/> <meta name="citation_reference" content="citation_journal_title=Nonlinear Dyn; citation_title=A tristable locally active memristor and its application in hopfield neural network; citation_author=C Li, Y Yang, X Yang, X Zi, F Xiao; citation_volume=108; citation_issue=2; citation_publication_date=2022; citation_pages=1697-1717; citation_doi=10.1007/s11071-022-07268-y; citation_id=CR45"/> <meta name="citation_reference" content="citation_journal_title=Nonlinear Dyn; citation_title=A memristive system and its applications in red–blue 3d glasses and image encryption algorithm with dna variation; citation_author=L Xiong, F Yang, J Mou, X An, X Zhang; citation_volume=107; citation_issue=3; citation_publication_date=2022; citation_pages=2911-2933; citation_doi=10.1007/s11071-021-07131-6; citation_id=CR46"/> <meta name="citation_reference" content="citation_journal_title=Chaos Solitons Fractals; citation_title=Simple colour image cryptosystem with very high level of security; citation_author=S Zhou, X Wang, M Wang, Y Zhang; citation_volume=141; citation_publication_date=2020; citation_doi=10.1016/j.chaos.2020.110225; citation_id=CR47"/> <meta name="citation_reference" content="citation_journal_title=Pramana; citation_title=A novel meminductor-based chaotic oscillating circuit and its dsp realisation for generating pn sequences; citation_author=C Han, Y Shen, Z Wu, G Wang; citation_volume=94; citation_issue=1; citation_publication_date=2020; citation_pages=101; citation_doi=10.1007/s12043-020-01969-y; citation_id=CR48"/> <meta name="citation_reference" content="citation_journal_title=Multimedia Syst; citation_title=A novel image encryption cryptosystem based on true random numbers and chaotic systems; citation_author=S Zhou, X Wang, Y Zhang, B Ge, M Wang, S Gao; citation_volume=28; citation_issue=1; citation_publication_date=2022; citation_pages=95-112; citation_doi=10.1007/s00530-021-00803-8; citation_id=CR49"/> <meta name="citation_reference" content="citation_journal_title=Chaos Solitons Fractals; citation_title=A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system; citation_author=Z Chen, Y Yong, Z Yuan; citation_volume=38; citation_issue=4; citation_publication_date=2008; citation_pages=1187-1196; citation_doi=10.1016/j.chaos.2007.01.058; citation_id=CR50"/> <meta name="citation_reference" content="citation_journal_title=J Math Anal Appl; citation_title=Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models - sciencedirect; citation_author=E Ahmed, AMA El-Sayed, HAA El-Saka; citation_volume=325; citation_issue=1; citation_publication_date=2007; citation_pages=542-553; citation_doi=10.1016/j.jmaa.2006.01.087; citation_id=CR51"/> <meta name="citation_author" content="Liu, Tianming"/> <meta name="citation_author_institution" content="School of Information Science and Engineering, Dalian Polytechnic University, Dalian, China"/> <meta name="citation_author" content="Sun, Bo"/> <meta name="citation_author_email" content="sunbo_0709@126.com"/> <meta name="citation_author_institution" content="School of Management, Dalian Polytechnic University, Dalian, China"/> <meta name="citation_author" content="Li, Peng"/> <meta name="citation_author_email" content="dlpulipeng@163.com"/> <meta name="citation_author_institution" content="School of Information Science and Engineering, Dalian Polytechnic University, Dalian, China"/> <meta name="citation_author" content="Ma, Tao"/> <meta name="citation_author_institution" content="School of Information Science and Engineering, Dalian Polytechnic University, Dalian, China"/> <meta name="citation_author" content="Ma, Yanjie"/> <meta name="citation_author_institution" content="School of Information Science and Engineering, Dalian Polytechnic University, Dalian, China"/> <meta name="format-detection" content="telephone=no"/> <meta property="og:url" content="https://link.springer.com/article/10.1007/s11036-023-02155-1"/> <meta property="og:type" content="article"/> <meta property="og:site_name" content="SpringerLink"/> <meta property="og:title" content="Multistability Analysis of a Fractional-Order Multi-Wing Chaotic System and its Circuit Realization - Mobile Networks and Applications"/> <meta property="og:description" content="The multi-scroll or multi-wing attractor generated by the chaotic system has a complicated structure. Based on the definition of conformal fractional-order, the Adomian decomposition method is used to solve the fractional-order multi-wing chaotic system. It is worth noting that this system has been found to have at least six multi-wing chaotic attractors with different shapes. The system parameters are used as bifurcation control parameters, and multiple bifurcation behaviors and multi-wing attractors can be observed. The results show that the 0.9-order chaotic system still has multiple stable phenomena, and some typical coexistence phenomena such as period and period, period and chaos, and chaos and chaos can all be found. Finally, an analog circuit was built on the Multisim simulation software, and the chaotic system successfully carry out on the DSP board. This research gives guidance on applying the conformable fractional-order theory to nonlinear systems."/> <meta property="og:image" content="https://static-content.springer.com/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig1_HTML.png"/> <meta name="format-detection" content="telephone=no"> <link rel="apple-touch-icon" sizes="180x180" href=/oscar-static/img/favicons/darwin/apple-touch-icon-92e819bf8a.png> <link rel="icon" type="image/png" sizes="192x192" href=/oscar-static/img/favicons/darwin/android-chrome-192x192-6f081ca7e5.png> <link rel="icon" type="image/png" sizes="32x32" href=/oscar-static/img/favicons/darwin/favicon-32x32-1435da3e82.png> <link rel="icon" type="image/png" sizes="16x16" href=/oscar-static/img/favicons/darwin/favicon-16x16-ed57f42bd2.png> <link rel="shortcut icon" data-test="shortcut-icon" href=/oscar-static/img/favicons/darwin/favicon-c6d59aafac.ico> <meta name="theme-color" content="#e6e6e6">   <link rel="stylesheet" media="print" 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href="https://link.springer.com/journal/11036/aims-and-scope" class="app-article-masthead__submission-link" data-track="click_aims_and_scope" data-track-action="aims and scope" data-track-context="article page" data-track-label="link"> Aims and scope <svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-arrow-right-medium"></use></svg> </a> <a href="https://submission.springernature.com/new-submission/11036/3" class="app-article-masthead__submission-link" data-track="click_submit_manuscript" data-track-context="article masthead on springerlink article page" data-track-action="submit manuscript" data-track-label="link"> Submit manuscript <svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-arrow-right-medium"></use></svg> </a> </div> </div> </div> </section> <div class="c-article-main u-container u-mt-24 u-mb-32 l-with-sidebar" id="main-content" data-component="article-container"> <main class="u-serif js-main-column" data-track-component="article body"> <div class="c-article-header"> <header> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Tianming-Liu-Aff1" data-author-popup="auth-Tianming-Liu-Aff1" data-author-search="Liu, Tianming">Tianming Liu</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Bo-Sun-Aff2" data-author-popup="auth-Bo-Sun-Aff2" data-author-search="Sun, Bo">Bo Sun</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li 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data-author-search="Ma, Tao">Tao Ma</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> & </li><li class="c-article-author-list__show-more" aria-label="Show all 5 authors for this article" title="Show all 5 authors for this article">…</li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Yanjie-Ma-Aff1" data-author-popup="auth-Yanjie-Ma-Aff1" data-author-search="Ma, Yanjie">Yanjie Ma</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul><button aria-expanded="false" class="c-article-author-list__button"><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-down-medium"></use></svg><span>Show authors</span></button> <div data-test="article-metrics"> <ul class="app-article-metrics-bar u-list-reset"> <li class="app-article-metrics-bar__item"> <p 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class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>The multi-scroll or multi-wing attractor generated by the chaotic system has a complicated structure. Based on the definition of conformal fractional-order, the Adomian decomposition method is used to solve the fractional-order multi-wing chaotic system. It is worth noting that this system has been found to have at least six multi-wing chaotic attractors with different shapes. The system parameters are used as bifurcation control parameters, and multiple bifurcation behaviors and multi-wing attractors can be observed. The results show that the 0.9-order chaotic system still has multiple stable phenomena, and some typical coexistence phenomena such as period and period, period and chaos, and chaos and chaos can all be found. Finally, an analog circuit was built on the Multisim simulation software, and the chaotic system successfully carry out on the DSP board. 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srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig5_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig5_HTML.png" alt="" loading="lazy" width="312" height="280"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6"><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 6</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig6_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig6_HTML.png" alt="" loading="lazy" width="312" height="270"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-7"><figure><figcaption><b id="Fig7" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 7</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig7_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig7_HTML.png" alt="" loading="lazy" width="312" height="137"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-8"><figure><figcaption><b id="Fig8" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 8</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig8_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig8_HTML.png" alt="" loading="lazy" width="312" height="269"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-9"><figure><figcaption><b id="Fig9" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 9</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig9_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig9_HTML.png" alt="" loading="lazy" width="312" height="122"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-10"><figure><figcaption><b id="Fig10" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 10</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig10_HTML.png" alt="" loading="lazy" width="312" height="99"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-11"><figure><figcaption><b id="Fig11" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 11</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig11_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig11_HTML.png" alt="" loading="lazy" width="312" height="116"></picture></div></div></figure></div><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-12"><figure><figcaption><b id="Fig12" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 12</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><picture><source type="image/webp" srcset="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig12_HTML.png?as=webp"><img src="//media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11036-023-02155-1/MediaObjects/11036_2023_2155_Fig12_HTML.png" alt="" loading="lazy" width="312" height="188"></picture></div></div></figure></div> </div> <div data-test="cobranding-download"> </div> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" 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1732308339, embedded_user: 'null' } }); </script> <div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">Yan W, He S, Wang H, Sun K (2015) Bifurcations and synchronization of the fractional-order simplified lorenz hyperchaotic system. J Appl Anal Comput 5(2):210–219</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3327526" aria-label="MathSciNet reference 1">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 1" href="http://scholar.google.com/scholar_lookup?&title=Bifurcations%20and%20synchronization%20of%20the%20fractional-order%20simplified%20lorenz%20hyperchaotic%20system&journal=J%20Appl%20Anal%20Comput&volume=5&issue=2&pages=210-219&publication_year=2015&author=Yan%2CW&author=He%2CS&author=Wang%2CH&author=Sun%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="2."><p class="c-article-references__text" id="ref-CR2">Gorenflo R, Mainardi F (2008) Fractional calculus: Integral and differential equations of fractional order. Mathematics 49(2):277–290</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 2" href="http://scholar.google.com/scholar_lookup?&title=Fractional%20calculus%3A%20Integral%20and%20differential%20equations%20of%20fractional%20order&journal=Mathematics&volume=49&issue=2&pages=277-290&publication_year=2008&author=Gorenflo%2CR&author=Mainardi%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="3."><p class="c-article-references__text" id="ref-CR3">Machado JT, Kiryakova V, Mainardi F (2011) Recent history of fractional calculus. Commun Nonlinear Sci Numer Simul 16(3):1140–1153</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.cnsns.2010.05.027" data-track-item_id="10.1016/j.cnsns.2010.05.027" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.cnsns.2010.05.027" aria-label="Article reference 3" data-doi="10.1016/j.cnsns.2010.05.027">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=2736622" aria-label="MathSciNet reference 3">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 3" href="http://scholar.google.com/scholar_lookup?&title=Recent%20history%20of%20fractional%20calculus&journal=Commun%20Nonlinear%20Sci%20Numer%20Simul&doi=10.1016%2Fj.cnsns.2010.05.027&volume=16&issue=3&pages=1140-1153&publication_year=2011&author=Machado%2CJT&author=Kiryakova%2CV&author=Mainardi%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="4."><p class="c-article-references__text" id="ref-CR4">Liu X, Sun C, Zhou M, Wu C, Peng B, Li P (2021) Reinforcement learning-based multislot double-threshold spectrum sensing with bayesian fusion for industrial big spectrum data. IEEE Trans Ind Inform 17(5):3391–3400. <a href="https://doi.org/10.1109/TII.2020.2987421" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/TII.2020.2987421">https://doi.org/10.1109/TII.2020.2987421</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/TII.2020.2987421" data-track-item_id="10.1109/TII.2020.2987421" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FTII.2020.2987421" aria-label="Article reference 4" data-doi="10.1109/TII.2020.2987421">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 4" href="http://scholar.google.com/scholar_lookup?&title=Reinforcement%20learning-based%20multislot%20double-threshold%20spectrum%20sensing%20with%20bayesian%20fusion%20for%20industrial%20big%20spectrum%20data&journal=IEEE%20Trans%20Ind%20Inform&doi=10.1109%2FTII.2020.2987421&volume=17&issue=5&pages=3391-3400&publication_year=2021&author=Liu%2CX&author=Sun%2CC&author=Zhou%2CM&author=Wu%2CC&author=Peng%2CB&author=Li%2CP"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="5."><p class="c-article-references__text" id="ref-CR5">Liu X, Sun C, Yau K-LA, Wu C (2022) Joint collaborative big spectrum data sensing and reinforcement learning based dynamic spectrum access for cognitive internet of vehicles. IEEE Trans Intell Transp Syst 1–11. <a href="https://doi.org/10.1109/TITS.2022.3175570" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/TITS.2022.3175570">https://doi.org/10.1109/TITS.2022.3175570</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="6."><p class="c-article-references__text" id="ref-CR6">Liu X, Ding H, Hu S (2021) Uplink resource allocation for noma-based hybrid spectrum access in 6g-enabled cognitive internet of things. IEEE Internet Things J 8(20):15049–15058. <a href="https://doi.org/10.1109/JIOT.2020.3007017" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/JIOT.2020.3007017">https://doi.org/10.1109/JIOT.2020.3007017</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/JIOT.2020.3007017" data-track-item_id="10.1109/JIOT.2020.3007017" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FJIOT.2020.3007017" aria-label="Article reference 6" data-doi="10.1109/JIOT.2020.3007017">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 6" href="http://scholar.google.com/scholar_lookup?&title=Uplink%20resource%20allocation%20for%20noma-based%20hybrid%20spectrum%20access%20in%206g-enabled%20cognitive%20internet%20of%20things&journal=IEEE%20Internet%20Things%20J&doi=10.1109%2FJIOT.2020.3007017&volume=8&issue=20&pages=15049-15058&publication_year=2021&author=Liu%2CX&author=Ding%2CH&author=Hu%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="7."><p class="c-article-references__text" id="ref-CR7">Li C, Sprott JC, Akgul A, Iu HHC, Zhao Y (2017) A new chaotic oscillator with free control. Chaos 27(8):083101</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.4997051" data-track-item_id="10.1063/1.4997051" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.4997051" aria-label="Article reference 7" data-doi="10.1063/1.4997051">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3681553" aria-label="MathSciNet reference 7">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 7" href="http://scholar.google.com/scholar_lookup?&title=A%20new%20chaotic%20oscillator%20with%20free%20control&journal=Chaos&doi=10.1063%2F1.4997051&volume=27&issue=8&publication_year=2017&author=Li%2CC&author=Sprott%2CJC&author=Akgul%2CA&author=Iu%2CHHC&author=Zhao%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="8."><p class="c-article-references__text" id="ref-CR8">Atman KG, Şirin H (2020) Nonlocal phenomena in quantum mechanics with fractional calculus. Rep Math Phys 86(2):263–270. <a href="https://doi.org/10.1016/S0034-4877(20)30075-6" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/S0034-4877(20)30075-6">https://doi.org/10.1016/S0034-4877(20)30075-6</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/S0034-4877(20)30075-6" data-track-item_id="10.1016/S0034-4877(20)30075-6" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2FS0034-4877%2820%2930075-6" aria-label="Article reference 8" data-doi="10.1016/S0034-4877(20)30075-6">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4169343" aria-label="MathSciNet reference 8">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 8" href="http://scholar.google.com/scholar_lookup?&title=Nonlocal%20phenomena%20in%20quantum%20mechanics%20with%20fractional%20calculus&journal=Rep%20Math%20Phys&doi=10.1016%2FS0034-4877%2820%2930075-6&volume=86&issue=2&pages=263-270&publication_year=2020&author=Atman%2CKG&author=%C5%9Eirin%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="9."><p class="c-article-references__text" id="ref-CR9">Liu X, Sun C, Yu W, Zhou M (2022) Reinforcement-learning-based dynamic spectrum access for software-defined cognitive industrial internet of things. IEEE Trans Ind Informa 18(6):4244–4253. <a href="https://doi.org/10.1109/TII.2021.3113949" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/TII.2021.3113949">https://doi.org/10.1109/TII.2021.3113949</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/TII.2021.3113949" data-track-item_id="10.1109/TII.2021.3113949" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FTII.2021.3113949" aria-label="Article reference 9" data-doi="10.1109/TII.2021.3113949">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 9" href="http://scholar.google.com/scholar_lookup?&title=Reinforcement-learning-based%20dynamic%20spectrum%20access%20for%20software-defined%20cognitive%20industrial%20internet%20of%20things&journal=IEEE%20Trans%20Ind%20Informa&doi=10.1109%2FTII.2021.3113949&volume=18&issue=6&pages=4244-4253&publication_year=2022&author=Liu%2CX&author=Sun%2CC&author=Yu%2CW&author=Zhou%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="10."><p class="c-article-references__text" id="ref-CR10">Lokenath D (2014) Recent applications of fractional calculus to science and engineering. Int J Math Math Sci 2003(54):3413–3442</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=2025566" aria-label="MathSciNet reference 10">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 10" href="http://scholar.google.com/scholar_lookup?&title=Recent%20applications%20of%20fractional%20calculus%20to%20science%20and%20engineering&journal=Int%20J%20Math%20Math%20Sci&volume=2003&issue=54&pages=3413-3442&publication_year=2014&author=Lokenath%2CD"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="11."><p class="c-article-references__text" id="ref-CR11">Kumar S, Matouk AE, Chaudhary H, Kant S (2021) Control and synchronization of fractional-order chaotic satellite systems using feedback and adaptive control techniques. Int J Adapt Control Signal Process 35(4):484–497. <a href="https://doi.org/10.1002/acs.3207" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1002/acs.3207">https://doi.org/10.1002/acs.3207</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1002/acs.3207" data-track-item_id="10.1002/acs.3207" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1002%2Facs.3207" aria-label="Article reference 11" data-doi="10.1002/acs.3207">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4246631" aria-label="MathSciNet reference 11">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 11" href="http://scholar.google.com/scholar_lookup?&title=Control%20and%20synchronization%20of%20fractional-order%20chaotic%20satellite%20systems%20using%20feedback%20and%20adaptive%20control%20techniques&journal=Int%20J%20Adapt%20Control%20Signal%20Process&doi=10.1002%2Facs.3207&volume=35&issue=4&pages=484-497&publication_year=2021&author=Kumar%2CS&author=Matouk%2CAE&author=Chaudhary%2CH&author=Kant%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="12."><p class="c-article-references__text" id="ref-CR12">Liu X, Sun Q, Lu W, Wu C, Ding H (2020) Big-data-based intelligent spectrum sensing for heterogeneous spectrum communications in 5g. IEEE Wirel Commun 27(5):67–73. <a href="https://doi.org/10.1109/MWC.001.1900493" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/MWC.001.1900493">https://doi.org/10.1109/MWC.001.1900493</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/MWC.001.1900493" data-track-item_id="10.1109/MWC.001.1900493" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FMWC.001.1900493" aria-label="Article reference 12" data-doi="10.1109/MWC.001.1900493">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 12" href="http://scholar.google.com/scholar_lookup?&title=Big-data-based%20intelligent%20spectrum%20sensing%20for%20heterogeneous%20spectrum%20communications%20in%205g&journal=IEEE%20Wirel%20Commun&doi=10.1109%2FMWC.001.1900493&volume=27&issue=5&pages=67-73&publication_year=2020&author=Liu%2CX&author=Sun%2CQ&author=Lu%2CW&author=Wu%2CC&author=Ding%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="13."><p class="c-article-references__text" id="ref-CR13">Xiang G, Yin D, Meng R, Cao C (2021) Predictive model for stress relaxation behavior of glassy polymers based on variable-order fractional calculus. Polym Adv Technol 32(2):703–713. <a href="https://doi.org/10.1002/pat.5123" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1002/pat.5123">https://doi.org/10.1002/pat.5123</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1002/pat.5123" data-track-item_id="10.1002/pat.5123" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1002%2Fpat.5123" aria-label="Article reference 13" data-doi="10.1002/pat.5123">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 13" href="http://scholar.google.com/scholar_lookup?&title=Predictive%20model%20for%20stress%20relaxation%20behavior%20of%20glassy%20polymers%20based%20on%20variable-order%20fractional%20calculus&journal=Polym%20Adv%20Technol&doi=10.1002%2Fpat.5123&volume=32&issue=2&pages=703-713&publication_year=2021&author=Xiang%2CG&author=Yin%2CD&author=Meng%2CR&author=Cao%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="14."><p class="c-article-references__text" id="ref-CR14">Lin H, Wang C, Chen C, Sun Y, Zhou C, Xu C, Hong Q (2021) Neural bursting and synchronization emulated by neural networks and circuits. IEEE Trans Circ Syst I Regular Pap 68(8):3397–3410. <a href="https://doi.org/10.1109/TCSI.2021.3081150" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/TCSI.2021.3081150">https://doi.org/10.1109/TCSI.2021.3081150</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1109/TCSI.2021.3081150" data-track-item_id="10.1109/TCSI.2021.3081150" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1109%2FTCSI.2021.3081150" aria-label="Article reference 14" data-doi="10.1109/TCSI.2021.3081150">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 14" href="http://scholar.google.com/scholar_lookup?&title=Neural%20bursting%20and%20synchronization%20emulated%20by%20neural%20networks%20and%20circuits&journal=IEEE%20Trans%20Circ%20Syst%20I%20Regular%20Pap&doi=10.1109%2FTCSI.2021.3081150&volume=68&issue=8&pages=3397-3410&publication_year=2021&author=Lin%2CH&author=Wang%2CC&author=Chen%2CC&author=Sun%2CY&author=Zhou%2CC&author=Xu%2CC&author=Hong%2CQ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="15."><p class="c-article-references__text" id="ref-CR15">Khalil R, Al Horani M, Yousef A, Sababheh M (2014) A new definition of fractional derivative. J Comput Appl Math 264:65–70. <a href="https://doi.org/10.1016/j.cam.2014.01.002" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.cam.2014.01.002">https://doi.org/10.1016/j.cam.2014.01.002</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.cam.2014.01.002" data-track-item_id="10.1016/j.cam.2014.01.002" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.cam.2014.01.002" aria-label="Article reference 15" data-doi="10.1016/j.cam.2014.01.002">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3164103" aria-label="MathSciNet reference 15">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 15" href="http://scholar.google.com/scholar_lookup?&title=A%20new%20definition%20of%20fractional%20derivative&journal=J%20Comput%20Appl%20Math&doi=10.1016%2Fj.cam.2014.01.002&volume=264&pages=65-70&publication_year=2014&author=Khalil%2CR&author=Al%20Horani%2CM&author=Yousef%2CA&author=Sababheh%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="16."><p class="c-article-references__text" id="ref-CR16">Abdeljawad T (2015) On conformable fractional calculus. J Comput Appl Math 279:57–66. <a href="https://doi.org/10.1016/j.cam.2014.10.016" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.cam.2014.10.016">https://doi.org/10.1016/j.cam.2014.10.016</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.cam.2014.10.016" data-track-item_id="10.1016/j.cam.2014.10.016" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.cam.2014.10.016" aria-label="Article reference 16" data-doi="10.1016/j.cam.2014.10.016">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3293309" aria-label="MathSciNet reference 16">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 16" href="http://scholar.google.com/scholar_lookup?&title=On%20conformable%20fractional%20calculus&journal=J%20Comput%20Appl%20Math&doi=10.1016%2Fj.cam.2014.10.016&volume=279&pages=57-66&publication_year=2015&author=Abdeljawad%2CT"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="17."><p class="c-article-references__text" id="ref-CR17">Wang Y (2018) Dynamic analysis and synchronization of conformable fractional-order chaotic systems. Eur Phys J Plus 133(11)</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="18."><p class="c-article-references__text" id="ref-CR18">Zhao D, Luo M (2017) General conformable fractional derivative and its physical interpretation. Calcolo 54(3):903–917. <a href="https://doi.org/10.1007/s10092-017-0213-8" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s10092-017-0213-8">https://doi.org/10.1007/s10092-017-0213-8</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s10092-017-0213-8" data-track-item_id="10.1007/s10092-017-0213-8" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s10092-017-0213-8" aria-label="Article reference 18" data-doi="10.1007/s10092-017-0213-8">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=3694729" aria-label="MathSciNet reference 18">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 18" href="http://scholar.google.com/scholar_lookup?&title=General%20conformable%20fractional%20derivative%20and%20its%20physical%20interpretation&journal=Calcolo&doi=10.1007%2Fs10092-017-0213-8&volume=54&issue=3&pages=903-917&publication_year=2017&author=Zhao%2CD&author=Luo%2CM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="19."><p class="c-article-references__text" id="ref-CR19">He S, Sun K, Mei X, Yan B, Xu S (2017) Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative. Eur Phys J Plus 132(1):36. <a href="https://doi.org/10.1140/epjp/i2017-11306-3" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1140/epjp/i2017-11306-3">https://doi.org/10.1140/epjp/i2017-11306-3</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjp/i2017-11306-3" data-track-item_id="10.1140/epjp/i2017-11306-3" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjp%2Fi2017-11306-3" aria-label="Article reference 19" data-doi="10.1140/epjp/i2017-11306-3">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 19" href="http://scholar.google.com/scholar_lookup?&title=Numerical%20analysis%20of%20a%20fractional-order%20chaotic%20system%20based%20on%20conformable%20fractional-order%20derivative&journal=Eur%20Phys%20J%20Plus&doi=10.1140%2Fepjp%2Fi2017-11306-3&volume=132&issue=1&publication_year=2017&author=He%2CS&author=Sun%2CK&author=Mei%2CX&author=Yan%2CB&author=Xu%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="20."><p class="c-article-references__text" id="ref-CR20">Ruan J, Sun K, Mou J, He S, Zhang L (2018) Fractional-order simplest memristor-based chaotic circuit with new derivative. Eur Phys J Plus 133(1):3</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjp/i2018-11828-0" data-track-item_id="10.1140/epjp/i2018-11828-0" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjp%2Fi2018-11828-0" aria-label="Article reference 20" data-doi="10.1140/epjp/i2018-11828-0">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 20" href="http://scholar.google.com/scholar_lookup?&title=Fractional-order%20simplest%20memristor-based%20chaotic%20circuit%20with%20new%20derivative&journal=Eur%20Phys%20J%20Plus&doi=10.1140%2Fepjp%2Fi2018-11828-0&volume=133&issue=1&publication_year=2018&author=Ruan%2CJ&author=Sun%2CK&author=Mou%2CJ&author=He%2CS&author=Zhang%2CL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="21."><p class="c-article-references__text" id="ref-CR21">Wang X, Wang S, Zhang Y, Luo C (2018) A one-time pad color image cryptosystem based on sha-3 and multiple chaotic systems. Optics Lasers Eng 103:1–8. <a href="https://doi.org/10.1016/j.optlaseng.2017.11.009" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.optlaseng.2017.11.009">https://doi.org/10.1016/j.optlaseng.2017.11.009</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.optlaseng.2017.11.009" data-track-item_id="10.1016/j.optlaseng.2017.11.009" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.optlaseng.2017.11.009" aria-label="Article reference 21" data-doi="10.1016/j.optlaseng.2017.11.009">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 21" href="http://scholar.google.com/scholar_lookup?&title=A%20one-time%20pad%20color%20image%20cryptosystem%20based%20on%20sha-3%20and%20multiple%20chaotic%20systems&journal=Optics%20Lasers%20Eng&doi=10.1016%2Fj.optlaseng.2017.11.009&volume=103&pages=1-8&publication_year=2018&author=Wang%2CX&author=Wang%2CS&author=Zhang%2CY&author=Luo%2CC"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="22."><p class="c-article-references__text" id="ref-CR22">Li X, Mou J, Cao Y, Banerjee S (2022) An optical image encryption algorithm based on a fractional-order laser hyperchaotic system. Int J Bifurcation Chaos 32(03):2250035. <a href="https://doi.org/10.1142/S0218127422500353" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1142/S0218127422500353">https://doi.org/10.1142/S0218127422500353</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1142/S0218127422500353" data-track-item_id="10.1142/S0218127422500353" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1142%2FS0218127422500353" aria-label="Article reference 22" data-doi="10.1142/S0218127422500353">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4392512" aria-label="MathSciNet reference 22">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 22" href="http://scholar.google.com/scholar_lookup?&title=An%20optical%20image%20encryption%20algorithm%20based%20on%20a%20fractional-order%20laser%20hyperchaotic%20system&journal=Int%20J%20Bifurcation%20Chaos&doi=10.1142%2FS0218127422500353&volume=32&issue=03&publication_year=2022&author=Li%2CX&author=Mou%2CJ&author=Cao%2CY&author=Banerjee%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="23."><p class="c-article-references__text" id="ref-CR23">Huang LL, Liu S, Xiang JH, Wang YuL (2021) Design and multistability analysis of five-value memristor based chaotic system with hidden attractors. Chin Phys B 30(10):100506–100506</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1088/1674-1056/ac1e13" data-track-item_id="10.1088/1674-1056/ac1e13" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1088%2F1674-1056%2Fac1e13" aria-label="Article reference 23" data-doi="10.1088/1674-1056/ac1e13">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 23" href="http://scholar.google.com/scholar_lookup?&title=Design%20and%20multistability%20analysis%20of%20five-value%20memristor%20based%20chaotic%20system%20with%20hidden%20attractors&journal=Chin%20Phys%20B&doi=10.1088%2F1674-1056%2Fac1e13&volume=30&issue=10&pages=100506-100506&publication_year=2021&author=Huang%2CLL&author=Liu%2CS&author=Xiang%2CJH&author=Wang%2CYuL"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="24."><p class="c-article-references__text" id="ref-CR24">Tabekoueng Njitacke Z, Sami Doubla I, Kengne J, Cheukem A (2020) Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse. Chaos 30(2):023101. <a href="https://doi.org/10.1063/1.5132280" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1063/1.5132280">https://doi.org/10.1063/1.5132280</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/1.5132280" data-track-item_id="10.1063/1.5132280" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F1.5132280" aria-label="Article reference 24" data-doi="10.1063/1.5132280">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4058926" aria-label="MathSciNet reference 24">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 24" href="http://scholar.google.com/scholar_lookup?&title=Coexistence%20of%20firing%20patterns%20and%20its%20control%20in%20two%20neurons%20coupled%20through%20an%20asymmetric%20electrical%20synapse&journal=Chaos&doi=10.1063%2F1.5132280&volume=30&issue=2&publication_year=2020&author=Tabekoueng%20Njitacke%2CZ&author=Sami%20Doubla%2CI&author=Kengne%2CJ&author=Cheukem%2CA"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="25."><p class="c-article-references__text" id="ref-CR25">(2022) An effective multiple-image encryption algorithm based on 3d cube and hyperchaotic map. J King Saud University Comput Inf Sci 34(4):1535–1551. <a href="https://doi.org/10.1016/j.jksuci.2022.01.017" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.jksuci.2022.01.017">https://doi.org/10.1016/j.jksuci.2022.01.017</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="26."><p class="c-article-references__text" id="ref-CR26">Natiq H, Banerjee S, Said MRM (2019) Cosine chaotification technique to enhance chaos and complexity of discrete systems. Eur Phys J Spec Top 228(1):185–194. <a href="https://doi.org/10.1140/epjst/e2019-800206-9" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1140/epjst/e2019-800206-9">https://doi.org/10.1140/epjst/e2019-800206-9</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjst/e2019-800206-9" data-track-item_id="10.1140/epjst/e2019-800206-9" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjst%2Fe2019-800206-9" aria-label="Article reference 26" data-doi="10.1140/epjst/e2019-800206-9">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 26" href="http://scholar.google.com/scholar_lookup?&title=Cosine%20chaotification%20technique%20to%20enhance%20chaos%20and%20complexity%20of%20discrete%20systems&journal=Eur%20Phys%20J%20Spec%20Top&doi=10.1140%2Fepjst%2Fe2019-800206-9&volume=228&issue=1&pages=185-194&publication_year=2019&author=Natiq%2CH&author=Banerjee%2CS&author=Said%2CMRM"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="27."><p class="c-article-references__text" id="ref-CR27">Li X, Mou J, Banerjee S, Wang Z, Cao Y (2022) Design and dsp implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption. Chaos, Solitons Fractals 159:112133. <a href="https://doi.org/10.1016/j.chaos.2022.112133" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.chaos.2022.112133">https://doi.org/10.1016/j.chaos.2022.112133</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.chaos.2022.112133" data-track-item_id="10.1016/j.chaos.2022.112133" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.chaos.2022.112133" aria-label="Article reference 27" data-doi="10.1016/j.chaos.2022.112133">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4414733" aria-label="MathSciNet reference 27">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 27" href="http://scholar.google.com/scholar_lookup?&title=Design%20and%20dsp%20implementation%20of%20a%20fractional-order%20detuned%20laser%20hyperchaotic%20circuit%20with%20applications%20in%20image%20encryption&journal=Chaos%2C%20Solitons%20Fractals&doi=10.1016%2Fj.chaos.2022.112133&volume=159&publication_year=2022&author=Li%2CX&author=Mou%2CJ&author=Banerjee%2CS&author=Wang%2CZ&author=Cao%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="28."><p class="c-article-references__text" id="ref-CR28">Lai Q, Kuate P, Liu F, Iu HC (2019) An extremely simple chaotic system with infinitely many coexisting attractors. Circ Syst II Express Briefs IEEE Trans PP(99):1–1. <a href="https://doi.org/10.1109/TCSII.2019.2927371" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1109/TCSII.2019.2927371">https://doi.org/10.1109/TCSII.2019.2927371</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="29."><p class="c-article-references__text" id="ref-CR29">Li C, Chen Z, Yang X, He S, Yang Y, Du J (2021) Self-reproducing dynamics in a two-dimensional discrete map. Eur Phys J Spec Top 230(7):1959–1970. <a href="https://doi.org/10.1140/epjs/s11734-021-00182-1" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1140/epjs/s11734-021-00182-1">https://doi.org/10.1140/epjs/s11734-021-00182-1</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjs/s11734-021-00182-1" data-track-item_id="10.1140/epjs/s11734-021-00182-1" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjs%2Fs11734-021-00182-1" aria-label="Article reference 29" data-doi="10.1140/epjs/s11734-021-00182-1">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 29" href="http://scholar.google.com/scholar_lookup?&title=Self-reproducing%20dynamics%20in%20a%20two-dimensional%20discrete%20map&journal=Eur%20Phys%20J%20Spec%20Top&doi=10.1140%2Fepjs%2Fs11734-021-00182-1&volume=230&issue=7&pages=1959-1970&publication_year=2021&author=Li%2CC&author=Chen%2CZ&author=Yang%2CX&author=He%2CS&author=Yang%2CY&author=Du%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="30."><p class="c-article-references__text" id="ref-CR30">Wu C, Sun K, Xiao Y (2021) A hyperchaotic map with multi-elliptic cavities based on modulation and coupling. Eur Phys J Spec Top 230(7):2011–2020. <a href="https://doi.org/10.1140/epjs/s11734-021-00126-9" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1140/epjs/s11734-021-00126-9">https://doi.org/10.1140/epjs/s11734-021-00126-9</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjs/s11734-021-00126-9" data-track-item_id="10.1140/epjs/s11734-021-00126-9" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjs%2Fs11734-021-00126-9" aria-label="Article reference 30" data-doi="10.1140/epjs/s11734-021-00126-9">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 30" href="http://scholar.google.com/scholar_lookup?&title=A%20hyperchaotic%20map%20with%20multi-elliptic%20cavities%20based%20on%20modulation%20and%20coupling&journal=Eur%20Phys%20J%20Spec%20Top&doi=10.1140%2Fepjs%2Fs11734-021-00126-9&volume=230&issue=7&pages=2011-2020&publication_year=2021&author=Wu%2CC&author=Sun%2CK&author=Xiao%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="31."><p class="c-article-references__text" id="ref-CR31">Li C, Li H, Xie W, Du J (2021) A s-type bistable locally active memristor model and its analog implementation in an oscillator circuit. Nonlinear Dyn 106(1):1041–1058. <a href="https://doi.org/10.1007/s11071-021-06814-4" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s11071-021-06814-4">https://doi.org/10.1007/s11071-021-06814-4</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s11071-021-06814-4" data-track-item_id="10.1007/s11071-021-06814-4" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s11071-021-06814-4" aria-label="Article reference 31" data-doi="10.1007/s11071-021-06814-4">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 31" href="http://scholar.google.com/scholar_lookup?&title=A%20s-type%20bistable%20locally%20active%20memristor%20model%20and%20its%20analog%20implementation%20in%20an%20oscillator%20circuit&journal=Nonlinear%20Dyn&doi=10.1007%2Fs11071-021-06814-4&volume=106&issue=1&pages=1041-1058&publication_year=2021&author=Li%2CC&author=Li%2CH&author=Xie%2CW&author=Du%2CJ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="32."><p class="c-article-references__text" id="ref-CR32">Zhou Y, Li C, Li W, Li H, Feng W, Qian K (2021) Image encryption algorithm with circle index table scrambling and partition diffusion. Nonlinear Dyn 103(2):2043–2061. <a href="https://doi.org/10.1007/s11071-021-06206-8" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s11071-021-06206-8">https://doi.org/10.1007/s11071-021-06206-8</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s11071-021-06206-8" data-track-item_id="10.1007/s11071-021-06206-8" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s11071-021-06206-8" aria-label="Article reference 32" data-doi="10.1007/s11071-021-06206-8">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 32" href="http://scholar.google.com/scholar_lookup?&title=Image%20encryption%20algorithm%20with%20circle%20index%20table%20scrambling%20and%20partition%20diffusion&journal=Nonlinear%20Dyn&doi=10.1007%2Fs11071-021-06206-8&volume=103&issue=2&pages=2043-2061&publication_year=2021&author=Zhou%2CY&author=Li%2CC&author=Li%2CW&author=Li%2CH&author=Feng%2CW&author=Qian%2CK"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="33."><p class="c-article-references__text" id="ref-CR33">Gao X, Mou J, Xiong L, Sha Y, Yan H, Cao Y (2022) A fast and efficient multiple images encryption based on single-channel encryption and chaotic system. Nonlinear Dyn 108:613–636. <a href="https://doi.org/10.1007/s11071-021-07192-7" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s11071-021-07192-7">https://doi.org/10.1007/s11071-021-07192-7</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s11071-021-07192-7" data-track-item_id="10.1007/s11071-021-07192-7" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s11071-021-07192-7" aria-label="Article reference 33" data-doi="10.1007/s11071-021-07192-7">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 33" href="http://scholar.google.com/scholar_lookup?&title=A%20fast%20and%20efficient%20multiple%20images%20encryption%20based%20on%20single-channel%20encryption%20and%20chaotic%20system&journal=Nonlinear%20Dyn&doi=10.1007%2Fs11071-021-07192-7&volume=108&pages=613-636&publication_year=2022&author=Gao%2CX&author=Mou%2CJ&author=Xiong%2CL&author=Sha%2CY&author=Yan%2CH&author=Cao%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="34."><p class="c-article-references__text" id="ref-CR34">Han X, Mou J, Jahanshahi H, Cao Y, Bu F (2022) A new set of hyperchaotic maps based on modulation and coupling. Eur Phys J Plus 137(4):523. <a href="https://doi.org/10.1140/epjp/s13360-022-02734-3" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1140/epjp/s13360-022-02734-3">https://doi.org/10.1140/epjp/s13360-022-02734-3</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjp/s13360-022-02734-3" data-track-item_id="10.1140/epjp/s13360-022-02734-3" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjp%2Fs13360-022-02734-3" aria-label="Article reference 34" data-doi="10.1140/epjp/s13360-022-02734-3">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 34" href="http://scholar.google.com/scholar_lookup?&title=A%20new%20set%20of%20hyperchaotic%20maps%20based%20on%20modulation%20and%20coupling&journal=Eur%20Phys%20J%20Plus&doi=10.1140%2Fepjp%2Fs13360-022-02734-3&volume=137&issue=4&publication_year=2022&author=Han%2CX&author=Mou%2CJ&author=Jahanshahi%2CH&author=Cao%2CY&author=Bu%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="35."><p class="c-article-references__text" id="ref-CR35">Wu C, Sun K, Xiao Y (2021) A hyperchaotic map with multi-elliptic cavities based on modulation and coupling. Eur Phys J Spec Top 230(7):2011–2020. <a href="https://doi.org/10.1140/epjs/s11734-021-00126-9" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1140/epjs/s11734-021-00126-9">https://doi.org/10.1140/epjs/s11734-021-00126-9</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1140/epjs/s11734-021-00126-9" data-track-item_id="10.1140/epjs/s11734-021-00126-9" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1140%2Fepjs%2Fs11734-021-00126-9" aria-label="Article reference 35" data-doi="10.1140/epjs/s11734-021-00126-9">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 35" href="http://scholar.google.com/scholar_lookup?&title=A%20hyperchaotic%20map%20with%20multi-elliptic%20cavities%20based%20on%20modulation%20and%20coupling&journal=Eur%20Phys%20J%20Spec%20Top&doi=10.1140%2Fepjs%2Fs11734-021-00126-9&volume=230&issue=7&pages=2011-2020&publication_year=2021&author=Wu%2CC&author=Sun%2CK&author=Xiao%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="36."><p class="c-article-references__text" id="ref-CR36">Zhang S, Zeng Y, Li Z (2018) One to four-wing chaotic attractors coined from a novel 3d fractional-order chaotic system with complex dynamics. Chin J Phys 56(3):793–806. <a href="https://doi.org/10.1016/j.cjph.2018.03.002" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.cjph.2018.03.002">https://doi.org/10.1016/j.cjph.2018.03.002</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.cjph.2018.03.002" data-track-item_id="10.1016/j.cjph.2018.03.002" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.cjph.2018.03.002" aria-label="Article reference 36" data-doi="10.1016/j.cjph.2018.03.002">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 36" href="http://scholar.google.com/scholar_lookup?&title=One%20to%20four-wing%20chaotic%20attractors%20coined%20from%20a%20novel%203d%20fractional-order%20chaotic%20system%20with%20complex%20dynamics&journal=Chin%20J%20Phys&doi=10.1016%2Fj.cjph.2018.03.002&volume=56&issue=3&pages=793-806&publication_year=2018&author=Zhang%2CS&author=Zeng%2CY&author=Li%2CZ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="37."><p class="c-article-references__text" id="ref-CR37">Li C-L, Zhou Y, Li H-M, Feng W, Du J-R (2021) Image encryption scheme with bit-level scrambling and multiplication diffusion. Multimedia Tools Appl 80(12):18479–18501. <a href="https://doi.org/10.1007/s11042-021-10631-7" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s11042-021-10631-7">https://doi.org/10.1007/s11042-021-10631-7</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s11042-021-10631-7" data-track-item_id="10.1007/s11042-021-10631-7" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s11042-021-10631-7" aria-label="Article reference 37" data-doi="10.1007/s11042-021-10631-7">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 37" href="http://scholar.google.com/scholar_lookup?&title=Image%20encryption%20scheme%20with%20bit-level%20scrambling%20and%20multiplication%20diffusion&journal=Multimedia%20Tools%20Appl&doi=10.1007%2Fs11042-021-10631-7&volume=80&issue=12&pages=18479-18501&publication_year=2021&author=Li%2CC-L&author=Zhou%2CY&author=Li%2CH-M&author=Feng%2CW&author=Du%2CJ-R"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="38."><p class="c-article-references__text" id="ref-CR38">Xiao Y, Sun K, Yu M, Xu X (2019) Dynamics of a new multi-cavity hyperchaotic map and its dsp implementation. Int J Bifurcation Chaos 29(14):1950194. <a href="https://doi.org/10.1142/S0218127419501943" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1142/S0218127419501943">https://doi.org/10.1142/S0218127419501943</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1142/S0218127419501943" data-track-item_id="10.1142/S0218127419501943" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1142%2FS0218127419501943" aria-label="Article reference 38" data-doi="10.1142/S0218127419501943">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4045901" aria-label="MathSciNet reference 38">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 38" href="http://scholar.google.com/scholar_lookup?&title=Dynamics%20of%20a%20new%20multi-cavity%20hyperchaotic%20map%20and%20its%20dsp%20implementation&journal=Int%20J%20Bifurcation%20Chaos&doi=10.1142%2FS0218127419501943&volume=29&issue=14&publication_year=2019&author=Xiao%2CY&author=Sun%2CK&author=Yu%2CM&author=Xu%2CX"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="39."><p class="c-article-references__text" id="ref-CR39">Zhang S, Zheng J, Wang X, Zeng Z, Peng X (2021) A novel nonideal flux-controlled memristor model for generating arbitrary multidouble-scroll and multi-double-wing attractors. Int J Bifurcation Chaos 31(06):2150086. <a href="https://doi.org/10.1142/S0218127421500863" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1142/S0218127421500863">https://doi.org/10.1142/S0218127421500863</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1142/S0218127421500863" data-track-item_id="10.1142/S0218127421500863" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1142%2FS0218127421500863" aria-label="Article reference 39" data-doi="10.1142/S0218127421500863">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 39" href="http://scholar.google.com/scholar_lookup?&title=A%20novel%20nonideal%20flux-controlled%20memristor%20model%20for%20generating%20arbitrary%20multidouble-scroll%20and%20multi-double-wing%20attractors&journal=Int%20J%20Bifurcation%20Chaos&doi=10.1142%2FS0218127421500863&volume=31&issue=06&publication_year=2021&author=Zhang%2CS&author=Zheng%2CJ&author=Wang%2CX&author=Zeng%2CZ&author=Peng%2CX"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="40."><p class="c-article-references__text" id="ref-CR40">Gao X, Mou J, Banerjee S, Cao Y, Xiong L, Chen X (2022) An effective multiple-image encryption algorithm based on 3d cube and hyperchaotic map. J King Saud University Comput Inf Sci 34(4):1535–1551. <a href="https://doi.org/10.1016/j.jksuci.2022.01.017" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.jksuci.2022.01.017">https://doi.org/10.1016/j.jksuci.2022.01.017</a></p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="41."><p class="c-article-references__text" id="ref-CR41">Gu S, Peng Q, Leng X, Du B (2021) A novel non-equilibrium memristorbased system with multi-wing attractors and multiple transient transitions. Chaos Interdiscip J Nonlinear Sci 31(3):033105. <a href="https://doi.org/10.1063/5.0039121" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1063/5.0039121">https://doi.org/10.1063/5.0039121</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1063/5.0039121" data-track-item_id="10.1063/5.0039121" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1063%2F5.0039121" aria-label="Article reference 41" data-doi="10.1063/5.0039121">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 41" href="http://scholar.google.com/scholar_lookup?&title=A%20novel%20non-equilibrium%20memristorbased%20system%20with%20multi-wing%20attractors%20and%20multiple%20transient%20transitions&journal=Chaos%20Interdiscip%20J%20Nonlinear%20Sci&doi=10.1063%2F5.0039121&volume=31&issue=3&publication_year=2021&author=Gu%2CS&author=Peng%2CQ&author=Leng%2CX&author=Du%2CB"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="42."><p class="c-article-references__text" id="ref-CR42">Bao B, Hu A, Bao H, Xu Q, Wu H (2018) Three-dimensional memristive hindmarsh-rose neuron model with hidden coexisting asymmetric behaviors. Complexity 4:1–11. <a href="https://doi.org/10.1155/2018/3872573" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1155/2018/3872573">https://doi.org/10.1155/2018/3872573</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1155/2018/3872573" data-track-item_id="10.1155/2018/3872573" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1155%2F2018%2F3872573" aria-label="Article reference 42" data-doi="10.1155/2018/3872573">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 42" href="http://scholar.google.com/scholar_lookup?&title=Three-dimensional%20memristive%20hindmarsh-rose%20neuron%20model%20with%20hidden%20coexisting%20asymmetric%20behaviors&journal=Complexity&doi=10.1155%2F2018%2F3872573&volume=4&pages=1-11&publication_year=2018&author=Bao%2CB&author=Hu%2CA&author=Bao%2CH&author=Xu%2CQ&author=Wu%2CH"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="43."><p class="c-article-references__text" id="ref-CR43">Xiong L, Zhang X, Sufen T, Qi L, Zhang P (2020) Experimental verification of a comparative research platform for various nonlinearity and weak signal detection based on a memristor-based chua’s system. Int J Bifurcation Chaos 30(13)</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="44."><p class="c-article-references__text" id="ref-CR44">Jia HY, Chen ZQ, Wei X (2013) Analysis and circuit implementation for the fractional-order lorenz system. Acta Physica Sinica –Chinese Edition–62(14):140503–113</p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="45."><p class="c-article-references__text" id="ref-CR45">Li C, Yang Y, Yang X, Zi X, Xiao F (2022) A tristable locally active memristor and its application in hopfield neural network. Nonlinear Dyn 108(2):1697–1717. <a href="https://doi.org/10.1007/s11071-022-07268-y" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s11071-022-07268-y">https://doi.org/10.1007/s11071-022-07268-y</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s11071-022-07268-y" data-track-item_id="10.1007/s11071-022-07268-y" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s11071-022-07268-y" aria-label="Article reference 45" data-doi="10.1007/s11071-022-07268-y">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 45" href="http://scholar.google.com/scholar_lookup?&title=A%20tristable%20locally%20active%20memristor%20and%20its%20application%20in%20hopfield%20neural%20network&journal=Nonlinear%20Dyn&doi=10.1007%2Fs11071-022-07268-y&volume=108&issue=2&pages=1697-1717&publication_year=2022&author=Li%2CC&author=Yang%2CY&author=Yang%2CX&author=Zi%2CX&author=Xiao%2CF"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="46."><p class="c-article-references__text" id="ref-CR46">Xiong L, Yang F, Mou J, An X, Zhang X (2022) A memristive system and its applications in red–blue 3d glasses and image encryption algorithm with dna variation. Nonlinear Dyn 107(3):2911–2933. <a href="https://doi.org/10.1007/s11071-021-07131-6" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s11071-021-07131-6">https://doi.org/10.1007/s11071-021-07131-6</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s11071-021-07131-6" data-track-item_id="10.1007/s11071-021-07131-6" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s11071-021-07131-6" aria-label="Article reference 46" data-doi="10.1007/s11071-021-07131-6">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 46" href="http://scholar.google.com/scholar_lookup?&title=A%20memristive%20system%20and%20its%20applications%20in%20red%E2%80%93blue%203d%20glasses%20and%20image%20encryption%20algorithm%20with%20dna%20variation&journal=Nonlinear%20Dyn&doi=10.1007%2Fs11071-021-07131-6&volume=107&issue=3&pages=2911-2933&publication_year=2022&author=Xiong%2CL&author=Yang%2CF&author=Mou%2CJ&author=An%2CX&author=Zhang%2CX"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="47."><p class="c-article-references__text" id="ref-CR47">Zhou S, Wang X, Wang M, Zhang Y (2020) Simple colour image cryptosystem with very high level of security. Chaos Solitons Fractals 141:110225. <a href="https://doi.org/10.1016/j.chaos.2020.110225" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1016/j.chaos.2020.110225">https://doi.org/10.1016/j.chaos.2020.110225</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.chaos.2020.110225" data-track-item_id="10.1016/j.chaos.2020.110225" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.chaos.2020.110225" aria-label="Article reference 47" data-doi="10.1016/j.chaos.2020.110225">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=4160504" aria-label="MathSciNet reference 47">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 47" href="http://scholar.google.com/scholar_lookup?&title=Simple%20colour%20image%20cryptosystem%20with%20very%20high%20level%20of%20security&journal=Chaos%20Solitons%20Fractals&doi=10.1016%2Fj.chaos.2020.110225&volume=141&publication_year=2020&author=Zhou%2CS&author=Wang%2CX&author=Wang%2CM&author=Zhang%2CY"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="48."><p class="c-article-references__text" id="ref-CR48">Han C, Shen Y, Wu Z, Wang G (2020) A novel meminductor-based chaotic oscillating circuit and its dsp realisation for generating pn sequences. Pramana 94(1):101. <a href="https://doi.org/10.1007/s12043-020-01969-y" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s12043-020-01969-y">https://doi.org/10.1007/s12043-020-01969-y</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s12043-020-01969-y" data-track-item_id="10.1007/s12043-020-01969-y" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s12043-020-01969-y" aria-label="Article reference 48" data-doi="10.1007/s12043-020-01969-y">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 48" href="http://scholar.google.com/scholar_lookup?&title=A%20novel%20meminductor-based%20chaotic%20oscillating%20circuit%20and%20its%20dsp%20realisation%20for%20generating%20pn%20sequences&journal=Pramana&doi=10.1007%2Fs12043-020-01969-y&volume=94&issue=1&publication_year=2020&author=Han%2CC&author=Shen%2CY&author=Wu%2CZ&author=Wang%2CG"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="49."><p class="c-article-references__text" id="ref-CR49">Zhou S, Wang X, Zhang Y, Ge B, Wang M, Gao S (2022) A novel image encryption cryptosystem based on true random numbers and chaotic systems. Multimedia Syst 28(1):95–112. <a href="https://doi.org/10.1007/s00530-021-00803-8" data-track="click_references" data-track-action="external reference" data-track-value="external reference" data-track-label="10.1007/s00530-021-00803-8">https://doi.org/10.1007/s00530-021-00803-8</a></p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="noopener" data-track-label="10.1007/s00530-021-00803-8" data-track-item_id="10.1007/s00530-021-00803-8" data-track-value="article reference" data-track-action="article reference" href="https://link.springer.com/doi/10.1007/s00530-021-00803-8" aria-label="Article reference 49" data-doi="10.1007/s00530-021-00803-8">Article</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 49" href="http://scholar.google.com/scholar_lookup?&title=A%20novel%20image%20encryption%20cryptosystem%20based%20on%20true%20random%20numbers%20and%20chaotic%20systems&journal=Multimedia%20Syst&doi=10.1007%2Fs00530-021-00803-8&volume=28&issue=1&pages=95-112&publication_year=2022&author=Zhou%2CS&author=Wang%2CX&author=Zhang%2CY&author=Ge%2CB&author=Wang%2CM&author=Gao%2CS"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="50."><p class="c-article-references__text" id="ref-CR50">Chen Z, Yong Y, Yuan Z (2008) A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system. Chaos Solitons Fractals 38(4):1187–1196</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.chaos.2007.01.058" data-track-item_id="10.1016/j.chaos.2007.01.058" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.chaos.2007.01.058" aria-label="Article reference 50" data-doi="10.1016/j.chaos.2007.01.058">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=2435612" aria-label="MathSciNet reference 50">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 50" href="http://scholar.google.com/scholar_lookup?&title=A%20single%20three-wing%20or%20four-wing%20chaotic%20attractor%20generated%20from%20a%20three-dimensional%20smooth%20quadratic%20autonomous%20system&journal=Chaos%20Solitons%20Fractals&doi=10.1016%2Fj.chaos.2007.01.058&volume=38&issue=4&pages=1187-1196&publication_year=2008&author=Chen%2CZ&author=Yong%2CY&author=Yuan%2CZ"> Google Scholar</a> </p></li><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="51."><p class="c-article-references__text" id="ref-CR51">Ahmed E, El-Sayed AMA, El-Saka HAA (2007) Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models - sciencedirect. J Math Anal Appl 325(1):542–553</p><p class="c-article-references__links u-hide-print"><a data-track="click_references" rel="nofollow noopener" data-track-label="10.1016/j.jmaa.2006.01.087" data-track-item_id="10.1016/j.jmaa.2006.01.087" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1016%2Fj.jmaa.2006.01.087" aria-label="Article reference 51" data-doi="10.1016/j.jmaa.2006.01.087">Article</a> <a data-track="click_references" rel="nofollow noopener" data-track-label="link" data-track-item_id="link" data-track-value="mathscinet reference" data-track-action="mathscinet reference" href="http://www.ams.org/mathscinet-getitem?mr=2273544" aria-label="MathSciNet reference 51">MathSciNet</a> <a data-track="click_references" data-track-action="google scholar reference" data-track-value="google scholar reference" data-track-label="link" data-track-item_id="link" rel="nofollow noopener" aria-label="Google Scholar reference 51" href="http://scholar.google.com/scholar_lookup?&title=Equilibrium%20points%2C%20stability%20and%20numerical%20solutions%20of%20fractional-order%20predator-prey%20and%20rabies%20models%20-%20sciencedirect&journal=J%20Math%20Anal%20Appl&doi=10.1016%2Fj.jmaa.2006.01.087&volume=325&issue=1&pages=542-553&publication_year=2007&author=Ahmed%2CE&author=El-Sayed%2CAMA&author=El-Saka%2CHAA"> Google Scholar</a> </p></li></ol><p class="c-article-references__download u-hide-print"><a data-track="click" data-track-action="download citation references" data-track-label="link" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1007/s11036-023-02155-1?format=refman&flavour=references">Download references<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p></div></div></div></section></div><section data-title="Acknowledgements"><div class="c-article-section" id="Ack1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Ack1">Acknowledgements</h2><div class="c-article-section__content" id="Ack1-content"><p>This work was supported by the National Natural Science Foundation of China (Grant Nos. 62061014); The Natural Science Foundation of Liaoning province(2020-MS-274); The Basic Scientific Research Projects of Colleges and Universities of Liaoning Province (Grant Nos. LJKZ0545)</p></div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">School of Information Science and Engineering, Dalian Polytechnic University, Dalian, 116034, China</p><p class="c-article-author-affiliation__authors-list">Tianming Liu, Peng Li, Tao Ma & Yanjie Ma</p></li><li id="Aff2"><p class="c-article-author-affiliation__address">School of Management, Dalian Polytechnic University, Dalian, 116034, China</p><p class="c-article-author-affiliation__authors-list">Bo Sun</p></li></ol><div class="u-js-hide u-hide-print" data-test="author-info"><span class="c-article__sub-heading">Authors</span><ol class="c-article-authors-search u-list-reset"><li id="auth-Tianming-Liu-Aff1"><span class="c-article-authors-search__title u-h3 js-search-name">Tianming Liu</span><div class="c-article-authors-search__list"><div class="c-article-authors-search__item c-article-authors-search__list-item--left"><a href="/search?dc.creator=Tianming%20Liu" class="c-article-button" data-track="click" data-track-action="author link - 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id="citeas">Cite this article</h3><p class="c-bibliographic-information__citation">Liu, T., Sun, B., Li, P. <i>et al.</i> Multistability Analysis of a Fractional-Order Multi-Wing Chaotic System and its Circuit Realization. <i>Mobile Netw Appl</i> (2024). https://doi.org/10.1007/s11036-023-02155-1</p><p class="c-bibliographic-information__download-citation u-hide-print"><a data-test="citation-link" data-track="click" data-track-action="download article citation" data-track-label="link" data-track-external="" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1007/s11036-023-02155-1?format=refman&flavour=citation">Download citation<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p><ul class="c-bibliographic-information__list" data-test="publication-history"><li class="c-bibliographic-information__list-item"><p>Accepted<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2022-10-27">27 October 2022</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Published<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2024-11-15">15 November 2024</time></span></p></li><li class="c-bibliographic-information__list-item c-bibliographic-information__list-item--full-width"><p><abbr title="Digital Object Identifier">DOI</abbr><span class="u-hide">: </span><span class="c-bibliographic-information__value">https://doi.org/10.1007/s11036-023-02155-1</span></p></li></ul><div data-component="share-box"><div class="c-article-share-box u-display-none" hidden=""><h3 class="c-article__sub-heading">Share this article</h3><p class="c-article-share-box__description">Anyone you share the following link with will be able to read this content:</p><button 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