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Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.authorAlves Gouveia, Marcio R. [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T13:23:33Z
dc.date.available2014-05-20T13:23:33Z
dc.date.issued2011-08-15
dc.description.abstractWe consider a quadratic Lienard equation with an unbounded homoclinic loop, which is a solution tending in forward and backward time to a non-hyperbolic equilibrium point located at infinity. Under small time-periodic perturbation, this equilibrium becomes a normally hyperbolic line of singularities at infinity. We show that the perturbed system may present homoclinic bifurcations, leading to the existence of transverse intersections between the stable and unstable manifolds of such a normally hyperbolic line of singularities. The global study concerning the infinity is performed using the Poincare compactification in polar coordinates, from which we obtain a system defined on a set equivalent to a solid torus in R(3), whose boundary plays the role of the infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff-Smale Theorem, a complex dynamical behaviour of the perturbed system solutions in the finite part of the phase space. Numerical simulations are performed in order to illustrate this behaviour, which could be called "the chaos arising from infinity", since it depends on the global structure of the Lienard equation, including the points at infinity. Although applied to a particular case, the analysis presented provides a geometrical approach to study periodic perturbations of homoclinic (or heteroclinic) loops to infinity of any planar polynomial vector field. (C) 2011 Elsevier B.V. All rights reserved.en
dc.description.affiliationUniv Estadual Paulista, UNESP, Fac Ciencias & Tecnol, Dept Matemat Estat & Comp, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, UNESP, Fac Ciencias & Tecnol, Dept Matemat Estat & Comp, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipPró-Reitoria de Pesquisa da UNESP (PROPe UNESP)
dc.description.sponsorshipIdCNPq: 305204/2009-2
dc.format.extent1402-1409
dc.identifierhttp://dx.doi.org/10.1016/j.physd.2011.06.006
dc.identifier.citationPhysica D-nonlinear Phenomena. Amsterdam: Elsevier B.V., v. 240, n. 17, p. 1402-1409, 2011.
dc.identifier.doi10.1016/j.physd.2011.06.006
dc.identifier.issn0167-2789
dc.identifier.lattes3757225669056317
dc.identifier.urihttp://hdl.handle.net/11449/7115
dc.identifier.wosWOS:000294579600010
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofPhysica D: Nonlinear Phenomena
dc.relation.ispartofjcr1.960
dc.relation.ispartofsjr0,861
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectForced Lienard equationen
dc.subjectPoincare compactificationen
dc.subjectMelnikov methoden
dc.subjectHomoclinic bifurcationen
dc.subjectChaotic dynamicsen
dc.titleTime-periodic perturbation of a Lienard equation with an unbounded homoclinic loopen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.lattes3757225669056317
unesp.author.orcid0000-0003-2269-7091[1]
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Ciências e Tecnologia, Presidente Prudentept
unesp.departmentMatemática e Computação - FCTpt

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