PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

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dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T13:23:32Z
dc.date.available2014-05-20T13:23:32Z
dc.date.issued2012-05-01
dc.description.abstractWe study periodic perturbations of planar quadratic vector fields having infinite heteroclinic cycles, consisting of an invariant straight line joining two saddle points at infinity and an arc of orbit also at infinity. The global study concerning the infinity of the perturbed system is performed by means of 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. It is shown that for certain type of periodic perturbation, there exist two differentiable curves in the parameter space for which the perturbed system presents heteroclinic tangencies and transversal intersections between the stable and unstable manifolds of two normally hyperbolic lines of singularities at infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the perturbed system solutions in a finite part of the phase space. Numerical simulations are performed for a particular example in order to illustrate this behavior, which could be called the chaos arising from infinity, because it depends on the global structure of the quadratic system, including the points at infinity.en
dc.description.affiliationUniv Estadual Paulista UNESP, Dept Matemat Estat & Comp, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista UNESP, Dept Matemat Estat & Comp, Fac Ciencias & Tecnol, 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.sponsorshipIdCNPq: 305204/2009-2
dc.format.extent1881-1899
dc.identifierhttp://dx.doi.org/10.3934/dcds.2012.32.1881
dc.identifier.citationDiscrete and Continuous Dynamical Systems. Springfield: Amer Inst Mathematical Sciences, v. 32, n. 5, p. 1881-1899, 2012.
dc.identifier.doi10.3934/dcds.2012.32.1881
dc.identifier.issn1078-0947
dc.identifier.lattes3757225669056317
dc.identifier.urihttp://hdl.handle.net/11449/7106
dc.identifier.wosWOS:000299997100021
dc.language.isoeng
dc.publisherAmer Inst Mathematical Sciences
dc.relation.ispartofDiscrete and Continuous Dynamical Systems
dc.relation.ispartofjcr0.976
dc.relation.ispartofsjr1,592
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectQuadratic systemen
dc.subjectinfinite heteroclinic cycleen
dc.subjectperiodic perturbationen
dc.subjectPoincare compactificationen
dc.subjectheteroclinic bifurcationen
dc.subjectchaotic dynamicsen
dc.titlePERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLESen
dc.typeArtigo
dcterms.licensehttp://www.aimsciences.org/journals/access.jsp?journalID=1
dcterms.rightsHolderAmer Inst Mathematical Sciences
unesp.author.lattes3757225669056317
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Ciências e Tecnologia, Presidente Prudentept
unesp.departmentMatemática e Computação - FCTpt

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Presidente Prudente - FCT - Faculdade de Ciências e Tecnologia