{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:06:29Z","timestamp":1753880789879,"version":"3.41.2"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e0o Paulo","doi-asserted-by":"publisher","award":["2019\/10269-3"],"award-info":[{"award-number":["2019\/10269-3"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["311355\/ 2018-8"],"award-info":[{"award-number":["311355\/ 2018-8"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,12,15]]},"abstract":"<jats:p> In this paper, we consider a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and an active memristive device. The circuit is described by a four-parameter system of ordinary differential equations. We study in detail the role of parameters in the dynamics of the system. Using the existence of first integrals, we show that the circuit may present a continuum of stable periodic orbits, which arise due to the occurrence of infinitely many simultaneous zero-Hopf bifurcations on a line of equilibria located in the region where the memristance is negative and, consequently, the memristive device is locally-active. These bifurcations lead to multistability, which is a difficult and interesting problem in applied models, since the final state of a solution depends crucially on its initial condition. We also study the control of multistability by varying a parameter related to the state variable of the memristive device. All analytical results obtained were corroborated by numerical simulations. <\/jats:p>","DOI":"10.1142\/s0218127421300457","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T11:30:05Z","timestamp":1638876605000},"source":"Crossref","is-referenced-by-count":3,"title":["Local-Activity and Simultaneous Zero-Hopf Bifurcations Leading to Multistability in a Memristive Circuit"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2269-7091","authenticated-orcid":false,"given":"Marcelo","family":"Messias","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica e Computa\u00e7\u00e3o, Faculdade de Ci\u00eancias e Tecnologia, Universidade Estadual Paulista, UNESP, 19060-900 P. Prudente, S\u00e3o Paulo, Brazil"}]},{"given":"Alisson de Carvalho","family":"Reinol","sequence":"additional","affiliation":[{"name":"Departamento Acad\u00eamico de Matem\u00e1tica, Universidade Tecnol\u00f3gica Federal do Paran\u00e1, UTFPR, 86812-460, Apucarana, Paran\u00e1, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2021,12,7]]},"reference":[{"key":"S0218127421300457BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/CNNA.2014.6888591"},{"key":"S0218127421300457BIB002","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2017.00081"},{"key":"S0218127421300457BIB003","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083337"},{"key":"S0218127421300457BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1976.10092"},{"key":"S0218127421300457BIB005","doi-asserted-by":"publisher","DOI":"10.13164\/re.2015.0319"},{"key":"S0218127421300457BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-55651-8"},{"key":"S0218127421300457BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741103012X"},{"key":"S0218127421300457BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410025521"},{"key":"S0218127421300457BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027076"},{"key":"S0218127421300457BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2014.02.007"},{"volume-title":"Averaging Methods in Nonlinear Dynamical Systems","year":"2007","author":"Sanders J. 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