Global dynamics of the Rikitake system
dc.contributor.author | Llibre, Jaume | |
dc.contributor.author | Messias, Marcelo [UNESP] | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.contributor.institution | Univ Autonoma Barcelona | |
dc.date.accessioned | 2014-05-20T13:23:33Z | |
dc.date.available | 2014-05-20T13:23:33Z | |
dc.date.issued | 2009-02-01 | |
dc.description.abstract | The 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.affiliation | UNESP, Fac Ciencias & Tecnol, Dept Matemat Estatist & Computacao, BR-19060900 Presidente Prudente, SP, Brazil | |
dc.description.affiliation | Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain | |
dc.description.affiliationUnesp | UNESP, Fac Ciencias & Tecnol, Dept Matemat Estatist & Computacao, BR-19060900 Presidente Prudente, SP, Brazil | |
dc.description.sponsorship | MEC/FEDER | |
dc.description.sponsorship | CICYT | |
dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
dc.description.sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) | |
dc.description.sponsorshipId | MEC/FEDER: MTM2005-06098-CO2-01 | |
dc.description.sponsorshipId | CICYT: 2005SGR 00550 | |
dc.description.sponsorshipId | CNPq: 478544/2007-3 | |
dc.format.extent | 241-252 | |
dc.identifier | http://dx.doi.org/10.1016/j.physd.2008.10.011 | |
dc.identifier.citation | Physica D-nonlinear Phenomena. Amsterdam: Elsevier B.V., v. 238, n. 3, p. 241-252, 2009. | |
dc.identifier.doi | 10.1016/j.physd.2008.10.011 | |
dc.identifier.issn | 0167-2789 | |
dc.identifier.lattes | 3757225669056317 | |
dc.identifier.uri | http://hdl.handle.net/11449/7116 | |
dc.identifier.wos | WOS:000263401900002 | |
dc.language.iso | eng | |
dc.publisher | Elsevier B.V. | |
dc.relation.ispartof | Physica D: Nonlinear Phenomena | |
dc.relation.ispartofjcr | 1.960 | |
dc.relation.ispartofsjr | 0,861 | |
dc.rights.accessRights | Acesso restrito | |
dc.source | Web of Science | |
dc.subject | Rikitake attractor | en |
dc.subject | Geodynamo | en |
dc.subject | Unbounded orbits | en |
dc.subject | Poincare compactification | en |
dc.subject | Strange attractor creation | en |
dc.subject | Lorenz attractor | en |
dc.title | Global dynamics of the Rikitake system | en |
dc.type | Artigo | |
dcterms.license | http://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy | |
dcterms.rightsHolder | Elsevier B.V. | |
unesp.author.lattes | 3757225669056317 | |
unesp.author.orcid | 0000-0002-9511-5999[1] | |
unesp.author.orcid | 0000-0003-2269-7091[2] | |
unesp.campus | Universidade Estadual Paulista (Unesp), Faculdade de Ciências e Tecnologia, Presidente Prudente | pt |
unesp.department | Matemática e Computação - FCT | pt |
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