{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T14:23:37Z","timestamp":1778077417300,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,16]],"date-time":"2019-02-16T00:00:00Z","timestamp":1550275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61473177"],"award-info":[{"award-number":["61473177"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61801271"],"award-info":[{"award-number":["61801271"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61703247"],"award-info":[{"award-number":["61703247"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a new memcapacitor model and its corresponding circuit emulator are proposed, based on which, a chaotic oscillator is designed and the system dynamic characteristics are investigated, both analytically and experimentally. Extreme multistability and coexisting attractors are observed in this complex system. The basins of attraction, multistability, bifurcations, Lyapunov exponents, and initial-condition-triggered similar bifurcation are analyzed. Finally, the memcapacitor-based chaotic oscillator is realized via circuit implementation with experimental results presented.<\/jats:p>","DOI":"10.3390\/e21020188","type":"journal-article","created":{"date-parts":[[2019,2,25]],"date-time":"2019-02-25T03:30:08Z","timestamp":1551065408000},"page":"188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Complex Dynamics in a Memcapacitor-Based Circuit"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2017-6030","authenticated-orcid":false,"given":"Fang","family":"Yuan","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuxia","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangyi","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Dou","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1381-7418","authenticated-orcid":false,"given":"Guanrong","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, City University Hong Kong, Hong Kong 999077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1109\/JPROC.2009.2021077","article-title":"Circuit elements with memory: Memristors, memcapacitors and meminductors","volume":"97","author":"Ventra","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1038\/nature06932","article-title":"The missing memristor found","volume":"453","author":"Strukov","year":"2008","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1809","DOI":"10.1109\/TED.2011.2126022","article-title":"Bistable non-volatile elastic membrane memcapacitor exhibiting chaotic behavior","volume":"58","author":"Pershin","year":"2011","journal-title":"IEEE Trans. Electron Dev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"213503","DOI":"10.1063\/1.3268433","article-title":"Analog memory capacitor based on field-configurable ion-doped polymers","volume":"95","author":"Lai","year":"2009","journal-title":"Appl. Phys. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1730047","DOI":"10.1142\/S0218127417300476","article-title":"Dynamic analysis of a physical SBT memristor-based chaotic circuit","volume":"27","author":"Guo","year":"2017","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7628","DOI":"10.3390\/e17117628","article-title":"A memristor-based complex lorenz system and its modified projective synchronization","volume":"17","author":"Wang","year":"2015","journal-title":"Entropy"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wang, S.B., Wang, X.Y., Zhou, Y.F., and Han, B. (2016). A memristor-based hyperchaotic complex Lu system and its adaptive complex generalized synchronization. Entropy, 18.","DOI":"10.3390\/e18020058"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6240","DOI":"10.3390\/e16126240","article-title":"Generation and nonlinear dynamical analyses of fractional-order memristor-based Lorenz systems","volume":"16","author":"Xi","year":"2014","journal-title":"Entropy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6464","DOI":"10.3390\/e16126464","article-title":"A memristive diode bridge-based canonical chua\u2019s circuit","volume":"16","author":"Chen","year":"2014","journal-title":"Entropy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"195430","DOI":"10.1103\/PhysRevB.81.195430","article-title":"Solid-state memcapacitive system with negative and diverging capacitance","volume":"81","author":"Pershin","year":"2010","journal-title":"Phys. Rev. B"},{"key":"ref_11","first-page":"228","article-title":"Behavioral modeling of memcapacitor","volume":"20","author":"Biolek","year":"2011","journal-title":"Radioengineering"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1049\/el.2010.0358","article-title":"Spice modeling of memcapacitor","volume":"46","author":"Biolek","year":"2010","journal-title":"Electron. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1016\/j.mejo.2014.08.002","article-title":"Memcapacitor response under step and sinusoidal voltage excitations","volume":"45","author":"Fouda","year":"2014","journal-title":"Microelectron. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1428","DOI":"10.1049\/el.2010.2309","article-title":"Mutator for transforming memristor into memcapacitor","volume":"46","author":"Biolek","year":"2010","journal-title":"Electron. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2765","DOI":"10.1007\/s00034-015-9995-6","article-title":"Boundary dynamics of memcapacitor in voltage-excited circuits and relaxation oscillators","volume":"34","author":"Fouda","year":"2015","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_16","first-page":"6504969","article-title":"Coexisting oscillation and extreme multistability for a memcapacitor-based circuit","volume":"2017","author":"Wang","year":"2017","journal-title":"Math. Probl. Eng."},{"key":"ref_17","first-page":"1101","article-title":"A coupled memcapacitor emulator-based relaxation oscillator","volume":"63","author":"Yu","year":"2016","journal-title":"IEEE Trans. Circuits Syst. II-Express Briefs"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s11071-016-2870-6","article-title":"Coexisting attractors in a memcapacitor-based chaotic oscillator","volume":"86","author":"Yuan","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"013110","DOI":"10.1063\/1.4973238","article-title":"Memcapacitor model and its application in chaotic oscillator with memristor","volume":"27","author":"Wang","year":"2017","journal-title":"Chaos"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"033103","DOI":"10.1063\/1.4975825","article-title":"Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis","volume":"27","author":"Yuan","year":"2017","journal-title":"Chaos"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1007\/s11071-017-3921-3","article-title":"A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications","volume":"91","author":"Rajagopal","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3566","DOI":"10.1038\/s41598-018-21205-3","article-title":"Snap-through transition of buckled graphene membranes for memcapacitor applications","volume":"8","author":"Yamaletdinov","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"770","DOI":"10.15388\/NA.2016.6.3","article-title":"On new chaotic and hyperchaotic systems: A literature survey","volume":"21","author":"Lassoued","year":"2017","journal-title":"Nonlinear Anal. Model. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1142\/S0218127408021233","article-title":"Complex dynamics in multistable systems","volume":"18","author":"Feudel","year":"2008","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"056206","DOI":"10.1103\/PhysRevE.83.056206","article-title":"Extreme multistability in a chemical model system","volume":"83","author":"Ngonghala","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1007\/s11071-017-3952-9","article-title":"Controlling extreme multistability of memristor emulator-based dynamical circuit in flux-charge domain","volume":"91","author":"Chen","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5935637","DOI":"10.1155\/2018\/5935637","article-title":"Memristor-based canonical Chua\u2019s circuit: Extreme multistability in voltage-current domain and its controllability in flux-charge domain","volume":"2018","author":"Bao","year":"2018","journal-title":"Complexity"},{"key":"ref_28","unstructured":"Boubaker, O., and Jafari, S. (2018). Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications, Elsevier Academic Press. [1st ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3702","DOI":"10.1007\/s00034-018-0750-7","article-title":"Hyperchaotic memcapacitor oscillator with infinite equilibria and coexisting attractors","volume":"37","author":"Rajagopal","year":"2018","journal-title":"Circuits Syst. Signal Process."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/188\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:32:42Z","timestamp":1760185962000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/188"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,16]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020188"],"URL":"https:\/\/doi.org\/10.3390\/e21020188","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,16]]}}}