The Hopf bifurcation in the Shimizu-Morioka system

Detalhes bibliográficos
Autor(a) principal: Llibre, Jaume
Data de Publicação: 2015
Outros Autores: Pessoa, Claudio [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://link.springer.com/article/10.1007%2Fs11071-014-1805-3
http://hdl.handle.net/11449/128854
Resumo: We study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu-Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions for different values of the parameters.
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spelling The Hopf bifurcation in the Shimizu-Morioka systemHopf bifurcationLimit cyclesBifurcation diagramWe study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu-Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions for different values of the parameters.MINECO/FEDER MTMAGAURICREA AcademiaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, SpainUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilMINECO/FEDER MTM: 2008-03437AGAUR: 2014SGR 568CAPES: Process 8333/13-0FAPESP: 2011/13152-8: FP7 PEOPLE-2012-IRSES: 316338FP7 PEOPLE-2012-IRSES: 318999SpringerUniv Autonoma BarcelonaUniversidade Estadual Paulista (Unesp)Llibre, JaumePessoa, Claudio [UNESP]2015-10-21T13:14:32Z2015-10-21T13:14:32Z2015-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2197-2205http://link.springer.com/article/10.1007%2Fs11071-014-1805-3Nonlinear Dynamics, v. 79, n. 3, p. 2197-2205, 2015.0924-090Xhttp://hdl.handle.net/11449/12885410.1007/s11071-014-1805-3WOS:00034924490003837249378865574240000-0001-6790-1055Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Dynamics4.339info:eu-repo/semantics/openAccess2022-01-05T14:21:37Zoai:repositorio.unesp.br:11449/128854Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:24:12.543870Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv The Hopf bifurcation in the Shimizu-Morioka system
title The Hopf bifurcation in the Shimizu-Morioka system
spellingShingle The Hopf bifurcation in the Shimizu-Morioka system
Llibre, Jaume
Hopf bifurcation
Limit cycles
Bifurcation diagram
title_short The Hopf bifurcation in the Shimizu-Morioka system
title_full The Hopf bifurcation in the Shimizu-Morioka system
title_fullStr The Hopf bifurcation in the Shimizu-Morioka system
title_full_unstemmed The Hopf bifurcation in the Shimizu-Morioka system
title_sort The Hopf bifurcation in the Shimizu-Morioka system
author Llibre, Jaume
author_facet Llibre, Jaume
Pessoa, Claudio [UNESP]
author_role author
author2 Pessoa, Claudio [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Univ Autonoma Barcelona
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Llibre, Jaume
Pessoa, Claudio [UNESP]
dc.subject.por.fl_str_mv Hopf bifurcation
Limit cycles
Bifurcation diagram
topic Hopf bifurcation
Limit cycles
Bifurcation diagram
description We study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu-Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions for different values of the parameters.
publishDate 2015
dc.date.none.fl_str_mv 2015-10-21T13:14:32Z
2015-10-21T13:14:32Z
2015-02-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://link.springer.com/article/10.1007%2Fs11071-014-1805-3
Nonlinear Dynamics, v. 79, n. 3, p. 2197-2205, 2015.
0924-090X
http://hdl.handle.net/11449/128854
10.1007/s11071-014-1805-3
WOS:000349244900038
3724937886557424
0000-0001-6790-1055
url http://link.springer.com/article/10.1007%2Fs11071-014-1805-3
http://hdl.handle.net/11449/128854
identifier_str_mv Nonlinear Dynamics, v. 79, n. 3, p. 2197-2205, 2015.
0924-090X
10.1007/s11071-014-1805-3
WOS:000349244900038
3724937886557424
0000-0001-6790-1055
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Dynamics
4.339
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 2197-2205
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128355336192000

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