Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

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dc.contributor.authorMessias, Marcelo [UNESP]
dc.contributor.authorAlves Gouveia, Marcio R. [UNESP]
dc.contributor.authorPessoa, Claudio [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T14:02:52Z
dc.date.available2014-05-20T14:02:52Z
dc.date.issued2012-07-01
dc.description.abstractWe present some global dynamical aspects of Shimizu-Morioka equations given by(x)Over dot = y, (y)Over dot = x - lambda y - xz, (z)Over dot = -alpha z + x(2),where (x,y,z)aae(3) are the state variables and lambda,alpha are real parameters. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. Using the Poincar, compactification of a polynomial vector field in ae(3), we give a complete description of the dynamics of Shimizu-Morioka equations at infinity. Then using analytical and numerical tools, we investigate for the case alpha=0 the existence of infinitely many singularly degenerate heteroclinic cycles, each one consisting of an invariant set formed by a line of equilibria together with a heteroclinic orbit connecting two of these equilibria. The dynamical consequences of the existence of these cycles are also investigated. The present study is part of an effort aiming to describe global properties of quadratic three-dimensional vector fields with chaotic dynamical behavior, as made for instance in (Dias et al. in Nonlinear Anal. Real World Appl. 11(5):3491-3500, 2010; Kokubu and Roussarie in J. Dyn. Differ. Equ. 16(2):513-557, 2004; Llibre and Messias in Physica D 238(3):241-252, 2009; Llibre et al. in J. Phys. A, Math. Theor. 41:275210, 2008; Llibre et al. in Int. J. Bifurc. Chaos Appl. Sci. Eng. 20(10):3137-3155, 2010; Lorenz in J. Atmos. Sci. 20:130-141, 1963; Lu et al. in Int. J. Bifurc. Chaos Appl. Sci. Eng. 14(5):1507-1537, 2004; Mello et al. in Chaos Solitons Fractals 37:1244-1255, 2008; Messias in J. Phys. A, Math. Theor. 42:115101, 2009; Messias et al. in TEMA Tend. Mat. Apl. Comput. 9(2):275-285, 2008).en
dc.description.affiliationUniv Estadual Paulista UNESP, Fac Ciencias & Tecnol, Dept Matemat Estat & Comp, FCT, Presidente Prudente, SP, Brazil
dc.description.affiliationUniv Estadual Paulista UNESP, Dept Matemat, Inst Biociencias Letras & Ciencias Exatas IBILCE, Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista UNESP, Fac Ciencias & Tecnol, Dept Matemat Estat & Comp, FCT, Presidente Prudente, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista UNESP, Dept Matemat, Inst Biociencias Letras & Ciencias Exatas IBILCE, Sao Jose do Rio Preto, 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.extent577-587
dc.identifierhttp://dx.doi.org/10.1007/s11071-011-0288-8
dc.identifier.citationNonlinear Dynamics. Dordrecht: Springer, v. 69, n. 1-2, p. 577-587, 2012.
dc.identifier.doi10.1007/s11071-011-0288-8
dc.identifier.issn0924-090X
dc.identifier.lattes3757225669056317
dc.identifier.lattes3724937886557424
dc.identifier.orcid0000-0001-6790-1055
dc.identifier.urihttp://hdl.handle.net/11449/22150
dc.identifier.wosWOS:000304651400045
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofNonlinear Dynamics
dc.relation.ispartofjcr4.339
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectShimizu-Morioka equationsen
dc.subjectPoincare compactificationen
dc.subjectDynamics at infinityen
dc.subjectSingularly degenerate heteroclinic cyclesen
dc.subjectChaotic dynamicsen
dc.titleDynamics at infinity and other global dynamical aspects of Shimizu-Morioka equationsen
dc.typeArtigo
dcterms.licensehttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dcterms.rightsHolderSpringer
unesp.author.lattes3757225669056317
unesp.author.lattes3724937886557424[3]
unesp.author.orcid0000-0003-2269-7091[1]
unesp.author.orcid0000-0001-6790-1055[3]
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Ciências e Tecnologia, Presidente Prudentept
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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Artigos - Matemática e Computação - FCT
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