Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator

Detalhes bibliográficos
Autor(a) principal: Llibre, Jaume
Data de Publicação: 2020
Outros Autores: Messias, Marcelo [UNESP], Reinol, Alisson C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s10883-020-09491-5
http://hdl.handle.net/11449/201869
Resumo: We perform a global dynamical analysis of a modified Nosé-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincaré compactification. Then using the averaging theory, we prove analytically the existence of a linearly stable periodic orbit which bifurcates from one of the infinite periodic orbits which exist in the integrable cases. Moreover, by a detailed numerical study, we show the existence of nested invariant tori around the bifurcating periodic orbit. Finally, starting with the integrable cases and increasing the parameter values, we show that chaotic dynamics may occur, due to the break of such an invariant tori, leading to the creation of chaotic seas surrounding regular regions in the phase space.
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spelling Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover OscillatorAveraging theoryChaotic dynamicsFirst integralInvariant toriNosé-Hoover oscillatorPeriodic orbitWe perform a global dynamical analysis of a modified Nosé-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincaré compactification. Then using the averaging theory, we prove analytically the existence of a linearly stable periodic orbit which bifurcates from one of the infinite periodic orbits which exist in the integrable cases. Moreover, by a detailed numerical study, we show the existence of nested invariant tori around the bifurcating periodic orbit. Finally, starting with the integrable cases and increasing the parameter values, we show that chaotic dynamics may occur, due to the break of such an invariant tori, leading to the creation of chaotic seas surrounding regular regions in the phase space.Departament de Matemàtiques Universitat Autònoma de Barcelona (UAB), BellaterraDepartamento de Matemática e Computação Universidade Estadual Paulista (UNESP)Departamento Acadêmico de Matemática Universidade Tecnológica Federal do Paraná UTFPRDepartamento de Matemática e Computação Universidade Estadual Paulista (UNESP)Universitat Autònoma de Barcelona (UAB)Universidade Estadual Paulista (Unesp)UTFPRLlibre, JaumeMessias, Marcelo [UNESP]Reinol, Alisson C.2020-12-12T02:44:00Z2020-12-12T02:44:00Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s10883-020-09491-5Journal of Dynamical and Control Systems.1573-86981079-2724http://hdl.handle.net/11449/20186910.1007/s10883-020-09491-52-s2.0-85086408356Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Dynamical and Control Systemsinfo:eu-repo/semantics/openAccess2024-06-19T14:31:52Zoai:repositorio.unesp.br:11449/201869Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:45:43.615087Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
title Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
spellingShingle Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
Llibre, Jaume
Averaging theory
Chaotic dynamics
First integral
Invariant tori
Nosé-Hoover oscillator
Periodic orbit
title_short Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
title_full Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
title_fullStr Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
title_full_unstemmed Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
title_sort Global Dynamics and Bifurcation of Periodic Orbits in a Modified Nosé-Hoover Oscillator
author Llibre, Jaume
author_facet Llibre, Jaume
Messias, Marcelo [UNESP]
Reinol, Alisson C.
author_role author
author2 Messias, Marcelo [UNESP]
Reinol, Alisson C.
author2_role author
author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona (UAB)
Universidade Estadual Paulista (Unesp)
UTFPR
dc.contributor.author.fl_str_mv Llibre, Jaume
Messias, Marcelo [UNESP]
Reinol, Alisson C.
dc.subject.por.fl_str_mv Averaging theory
Chaotic dynamics
First integral
Invariant tori
Nosé-Hoover oscillator
Periodic orbit
topic Averaging theory
Chaotic dynamics
First integral
Invariant tori
Nosé-Hoover oscillator
Periodic orbit
description We perform a global dynamical analysis of a modified Nosé-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincaré compactification. Then using the averaging theory, we prove analytically the existence of a linearly stable periodic orbit which bifurcates from one of the infinite periodic orbits which exist in the integrable cases. Moreover, by a detailed numerical study, we show the existence of nested invariant tori around the bifurcating periodic orbit. Finally, starting with the integrable cases and increasing the parameter values, we show that chaotic dynamics may occur, due to the break of such an invariant tori, leading to the creation of chaotic seas surrounding regular regions in the phase space.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T02:44:00Z
2020-12-12T02:44:00Z
2020-01-01
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://dx.doi.org/10.1007/s10883-020-09491-5
Journal of Dynamical and Control Systems.
1573-8698
1079-2724
http://hdl.handle.net/11449/201869
10.1007/s10883-020-09491-5
2-s2.0-85086408356
url http://dx.doi.org/10.1007/s10883-020-09491-5
http://hdl.handle.net/11449/201869
identifier_str_mv Journal of Dynamical and Control Systems.
1573-8698
1079-2724
10.1007/s10883-020-09491-5
2-s2.0-85086408356
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Dynamical and Control Systems
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
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
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