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On the Existence of Limit Cycles and Relaxation Oscillations in a 3D van der Pol-like Memristor Oscillator

dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.authorMaciel, Anderson L.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Federal de Sergipe (UFS)
dc.date.accessioned2018-12-11T17:13:30Z
dc.date.available2018-12-11T17:13:30Z
dc.date.issued2017-06-30
dc.description.abstractWe study a van der Pol-like memristor oscillator, obtained by substituting a Chua's diode with an active controlled memristor in a van der Pol oscillator with Chua's diode. The mathematical model for the studied circuit is given by a three-dimensional piecewise linear system of ordinary differential equations, depending on five parameters. We show that this system has a line of equilibria given by the z-Axis and the phase space R3 is foliated by invariant planes transverse to this line, which implies that the dynamics is essentially two-dimensional. We also show that in each of these invariant planes may occur limit cycles and relaxation oscillations (that is, nonsinusoidal repetitive (periodic) solutions), depending on the parameter values. Hence, the oscillator studied here, constructed with a memristor, is also a relaxation oscillator, as the original van der Pol oscillator, although with a main difference: in the case of the memristor oscillator, an infinity of oscillations are produced, one in each invariant plane, depending on the initial condition considered. We also give conditions for the nonexistence of oscillations, depending on the position of the invariant planes in the phase space.en
dc.description.affiliationDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP Universidade Estadual Paulista
dc.description.affiliationDepartamento de Matemática Centro de Ciências Naturais e Exatas UFSM Universidade Federal de Santa Maria
dc.description.affiliationUnespDepartamento de Matemática e Computação Faculdade de Ciências e Tecnologia UNESP Universidade Estadual Paulista
dc.identifierhttp://dx.doi.org/10.1142/S0218127417501024
dc.identifier.citationInternational Journal of Bifurcation and Chaos, v. 27, n. 7, 2017.
dc.identifier.doi10.1142/S0218127417501024
dc.identifier.issn0218-1274
dc.identifier.lattes3757225669056317
dc.identifier.scopus2-s2.0-85025105345
dc.identifier.urihttp://hdl.handle.net/11449/174931
dc.language.isoeng
dc.relation.ispartofInternational Journal of Bifurcation and Chaos
dc.relation.ispartofsjr0,568
dc.rights.accessRightsAcesso restrito
dc.sourceScopus
dc.subjectChua's oscillator
dc.subjectmemristor
dc.subjectpiecewise linear systems
dc.subjectrelaxation oscillator
dc.subjectVan der Pol oscillator
dc.titleOn the Existence of Limit Cycles and Relaxation Oscillations in a 3D van der Pol-like Memristor Oscillatoren
dc.typeArtigo
unesp.author.lattes3757225669056317
unesp.departmentMatemática e Computação - FCTpt

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