Periodic orbits, invariant tori and chaotic behavior in certain nonequilibrium quadratic three-dimensional differential systems

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dc.contributor.authorReinol, Alisson C. [UNESP]
dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2018-12-11T17:18:21Z
dc.date.available2018-12-11T17:18:21Z
dc.date.issued2018-01-01
dc.description.abstractIn (Jafari et al, Phys Lett A 377(9):699-702, 2013) the authors gave the expressions of seventeen classes of quadratic differential systems defined in R3, depending on one real parameter a, which present chaotic behavior even without having any equilibrium point, for suitable choices of the parameter a > 0. In that paper, such systems are denoted by NE1 to NE17. As these systems have no equilibrium points, a natural question arises: how chaotic motion is generated in their nonequilibrium phase spaces? In this note we combine analytical and numerical results in order to study the integrability and dynamics of systems NE1, NE6, NE8 and NE9 among those listed in Jafari et al. (2013). We show that they exhibit a quite similar dynamical behavior and, consequently, the mechanisms for birth of chaos in these systems are similar. In this way, we intend to give at least a partial answer to the above question and contribute to better understand the complicated dynamics of the considered systems, in particular concerning the existence of periodic orbits and invariant tori and the emergence of chaotic behavior. The periodic orbits are studied using the Averaging Theory while the invariant tori are proved to exist via KAM Theorem. The chaotic dynamics arises from the broken of some of these invariant tori.en
dc.description.affiliationDepartamento de Matemática Universidade Estadual Paulista (UNESP) Instituto de Biociências Letras e Ciências Exatas
dc.description.affiliationFaculdade de Ciências e Tecnologia Departamento de Matemática e Computação Universidade Estadual Paulista (UNESP)
dc.description.affiliationUnespDepartamento de Matemática Universidade Estadual Paulista (UNESP) Instituto de Biociências Letras e Ciências Exatas
dc.description.affiliationUnespFaculdade de Ciências e Tecnologia Departamento de Matemática e Computação Universidade Estadual Paulista (UNESP)
dc.format.extent299-326
dc.identifierhttp://dx.doi.org/10.1007/978-3-319-71243-7_13
dc.identifier.citationStudies in Systems, Decision and Control, v. 133, p. 299-326.
dc.identifier.doi10.1007/978-3-319-71243-7_13
dc.identifier.issn2198-4190
dc.identifier.issn2198-4182
dc.identifier.lattes3757225669056317
dc.identifier.scopus2-s2.0-85042720139
dc.identifier.urihttp://hdl.handle.net/11449/175968
dc.language.isoeng
dc.relation.ispartofStudies in Systems, Decision and Control
dc.relation.ispartofsjr0,102
dc.relation.ispartofsjr0,102
dc.rights.accessRightsAcesso restrito
dc.sourceScopus
dc.subjectAveraging theory
dc.subjectChaotic dynamics
dc.subjectInvariant algebraic surfaces
dc.subjectInvariant tori
dc.subjectKAM theorem
dc.subjectPeriodic orbits
dc.titlePeriodic orbits, invariant tori and chaotic behavior in certain nonequilibrium quadratic three-dimensional differential systemsen
dc.typeCapítulo de livro
unesp.author.lattes3757225669056317

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