{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:53:56Z","timestamp":1760784836843,"version":"3.40.5"},"reference-count":54,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T00:00:00Z","timestamp":1587600000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,4,23]]},"abstract":"<jats:p>Symmetry is an important property found in a large number of nonlinear systems. The study of chaotic systems with symmetry is well documented. However, the literature is unfortunately very poor concerning the dynamics of such systems when their symmetry is altered or broken. In this paper, we investigate the dynamics of a simple jerk system with hyperbolic tangent nonlinearity (Kengne et al., Chaos Solitons, and Fractals, 2017) whose symmetry is broken by adding a constant term modeling an external excitation force. We demonstrate that the modified system experiences several unusual and striking nonlinear phenomena including coexisting bifurcation branches, hysteretic dynamics, coexisting asymmetric bubbles, critical transitions, and multiple (i.e., up to six) coexisting asymmetric attractors for some suitable ranges of system parameters. These features are highlighted by exploiting common nonlinear analysis tools such as graphs of largest Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction. The control of multistability is investigated by using the method of linear augmentation. We demonstrate that the multistable system can be converted to a monostable state by smoothly adjusting the coupling parameter. The theoretical results are confirmed by performing a series of PSpice simulations based on an electronic analogue of the system.<\/jats:p>","DOI":"10.1155\/2020\/2340934","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T23:33:24Z","timestamp":1587684804000},"page":"1-24","source":"Crossref","is-referenced-by-count":10,"title":["Symmetry Breaking, Coexisting Bubbles, Multistability, and Its Control for a Simple Jerk System with Hyperbolic Tangent Nonlinearity"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9197-8711","authenticated-orcid":true,"given":"L\u00e9andre Kamdjeu","family":"Kengne","sequence":"first","affiliation":[{"name":"Unit\u00e9 de Recherche d\u2019Automatique et Informatique Appliqu\u00e9e (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon"},{"name":"Unit\u00e9 de Recherche de Mati\u00e8re Condens\u00e9e, d\u2019Electronique et de Traitement du Signal (UR-MACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"given":"Jacques","family":"Kengne","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche d\u2019Automatique et Informatique Appliqu\u00e9e (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon"}]},{"given":"Justin Roger","family":"Mboupda Pone","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche d\u2019Automatique et Informatique Appliqu\u00e9e (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1236-1789","authenticated-orcid":true,"given":"Herv\u00e9 Thierry","family":"Kamdem Tagne","sequence":"additional","affiliation":[{"name":"Unit\u00e9 de Recherche de M\u00e9canique et de Mod\u00e9lisation des Syst\u00e8mes Physiques (UR-2MSP), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]}],"member":"311","reference":[{"year":"1994","key":"1"},{"year":"1995","key":"2"},{"year":"1995","key":"3"},{"year":"2010","key":"4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2013.08.018"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1142\/s021812741650098x"},{"issue":"9","key":"7","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1109\/TCSII.2016.2534698","volume":"63","year":"2016","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2016.06.111"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127416500693"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2014.02.007"},{"issue":"4","key":"11","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1142\/S0218127493000805","volume":"3","year":"1993","journal-title":"Int. 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