Global dynamics of the Rikitake system

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dc.contributor.authorLlibre, Jaume
dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniv Autonoma Barcelona
dc.date.accessioned2014-05-20T13:23:33Z
dc.date.available2014-05-20T13:23:33Z
dc.date.issued2009-02-01
dc.description.abstractThe Rikitake system is a three dimensional vector field obtained experimentally from a two-disk dynamo apparatus, which models the geomagnetic field and is used to explain the known irregular switch in its polarity. The system has a 3-dimensional Lorenz type chaotic attractor around its two singular points. However this attractor is not bounded by any ellipsoidal surface as in the Lorenz attractor. In this paper, by using the Poincare compactification for polynomial vector fields in R(3) we study the dynamics of the Rikitake system at infinity, showing that there are orbits which escape to, or come from, infinity, instead of going towards the attractor. Moreover we study, for particular values of the parameters, the flow over two invariant planes, and describe the global flow of the system when it has two independent first integrals and thus is completely integrable. The global analysis performed, allows us to give a numerical description of the creation of Rikitake attractor. (c) 2008 Elsevier B.V. All rights reserved.en
dc.description.affiliationUNESP, Fac Ciencias & Tecnol, Dept Matemat Estatist & Computacao, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
dc.description.affiliationUnespUNESP, Fac Ciencias & Tecnol, Dept Matemat Estatist & Computacao, BR-19060900 Presidente Prudente, SP, Brazil
dc.description.sponsorshipMEC/FEDER
dc.description.sponsorshipCICYT
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipIdMEC/FEDER: MTM2005-06098-CO2-01
dc.description.sponsorshipIdCICYT: 2005SGR 00550
dc.description.sponsorshipIdCNPq: 478544/2007-3
dc.format.extent241-252
dc.identifierhttp://dx.doi.org/10.1016/j.physd.2008.10.011
dc.identifier.citationPhysica D-nonlinear Phenomena. Amsterdam: Elsevier B.V., v. 238, n. 3, p. 241-252, 2009.
dc.identifier.doi10.1016/j.physd.2008.10.011
dc.identifier.issn0167-2789
dc.identifier.lattes3757225669056317
dc.identifier.urihttp://hdl.handle.net/11449/7116
dc.identifier.wosWOS:000263401900002
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.subjectRikitake attractoren
dc.subjectGeodynamoen
dc.subjectUnbounded orbitsen
dc.subjectPoincare compactificationen
dc.subjectStrange attractor creationen
dc.subjectLorenz attractoren
dc.titleGlobal dynamics of the Rikitake systemen
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.orcid0000-0002-9511-5999[1]
unesp.author.orcid0000-0003-2269-7091[2]
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Ciências e Tecnologia, Presidente Prudentept
unesp.departmentMatemática e Computação - FCTpt

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