On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator

Detalhes bibliográficos
Autor(a) principal: Messias, Marcelo [UNESP]
Data de Publicação: 2018
Outros Autores: Reinol, Alisson C. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s11071-018-4125-1
http://hdl.handle.net/11449/175881
Resumo: We consider the well-known Sprott A system, which is a special case of the widely studied Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown to present chaotic behavior, even in the absence of an equilibrium point. In this paper, we prove that, for a≠ 0 , the Sprott A system has neither invariant algebraic surfaces nor polynomial first integrals. For a> 0 small, by using the averaging method we prove the existence of a linearly stable periodic orbit, which bifurcates from a non-isolated zero-Hopf equilibrium point located at the origin. Moreover, we show numerically the existence of nested invariant tori surrounding this periodic orbit. Thus, we observe that these dynamical elements and their perturbation play an important role in the occurrence of chaotic behavior in the Sprott A system.
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spelling On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillatorAveraging methodChaotic behaviorInvariant algebraic surfacesNested invariant toriNosé–Hoover oscillatorPeriodic orbitsSprott A systemWe consider the well-known Sprott A system, which is a special case of the widely studied Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown to present chaotic behavior, even in the absence of an equilibrium point. In this paper, we prove that, for a≠ 0 , the Sprott A system has neither invariant algebraic surfaces nor polynomial first integrals. For a> 0 small, by using the averaging method we prove the existence of a linearly stable periodic orbit, which bifurcates from a non-isolated zero-Hopf equilibrium point located at the origin. Moreover, we show numerically the existence of nested invariant tori surrounding this periodic orbit. Thus, we observe that these dynamical elements and their perturbation play an important role in the occurrence of chaotic behavior in the Sprott A system.Departamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista (UNESP)Departamento de Matemática Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP)Departamento de Matemática e Computação Faculdade de Ciências e Tecnologia Universidade Estadual Paulista (UNESP)Departamento de Matemática Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP)Universidade Estadual Paulista (Unesp)Messias, Marcelo [UNESP]Reinol, Alisson C. [UNESP]2018-12-11T17:17:59Z2018-12-11T17:17:59Z2018-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1287-1297application/pdfhttp://dx.doi.org/10.1007/s11071-018-4125-1Nonlinear Dynamics, v. 92, n. 3, p. 1287-1297, 2018.1573-269X0924-090Xhttp://hdl.handle.net/11449/17588110.1007/s11071-018-4125-12-s2.0-850420699642-s2.0-85042069964.pdf3757225669056317Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Dynamicsinfo:eu-repo/semantics/openAccess2024-06-19T14:32:05Zoai:repositorio.unesp.br:11449/175881Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:26:09.868186Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
title On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
spellingShingle On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
Messias, Marcelo [UNESP]
Averaging method
Chaotic behavior
Invariant algebraic surfaces
Nested invariant tori
Nosé–Hoover oscillator
Periodic orbits
Sprott A system
title_short On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
title_full On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
title_fullStr On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
title_full_unstemmed On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
title_sort On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
author Messias, Marcelo [UNESP]
author_facet Messias, Marcelo [UNESP]
Reinol, Alisson C. [UNESP]
author_role author
author2 Reinol, Alisson C. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Messias, Marcelo [UNESP]
Reinol, Alisson C. [UNESP]
dc.subject.por.fl_str_mv Averaging method
Chaotic behavior
Invariant algebraic surfaces
Nested invariant tori
Nosé–Hoover oscillator
Periodic orbits
Sprott A system
topic Averaging method
Chaotic behavior
Invariant algebraic surfaces
Nested invariant tori
Nosé–Hoover oscillator
Periodic orbits
Sprott A system
description We consider the well-known Sprott A system, which is a special case of the widely studied Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown to present chaotic behavior, even in the absence of an equilibrium point. In this paper, we prove that, for a≠ 0 , the Sprott A system has neither invariant algebraic surfaces nor polynomial first integrals. For a> 0 small, by using the averaging method we prove the existence of a linearly stable periodic orbit, which bifurcates from a non-isolated zero-Hopf equilibrium point located at the origin. Moreover, we show numerically the existence of nested invariant tori surrounding this periodic orbit. Thus, we observe that these dynamical elements and their perturbation play an important role in the occurrence of chaotic behavior in the Sprott A system.
publishDate 2018
dc.date.none.fl_str_mv 2018-12-11T17:17:59Z
2018-12-11T17:17:59Z
2018-05-01
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/s11071-018-4125-1
Nonlinear Dynamics, v. 92, n. 3, p. 1287-1297, 2018.
1573-269X
0924-090X
http://hdl.handle.net/11449/175881
10.1007/s11071-018-4125-1
2-s2.0-85042069964
2-s2.0-85042069964.pdf
3757225669056317
url http://dx.doi.org/10.1007/s11071-018-4125-1
http://hdl.handle.net/11449/175881
identifier_str_mv Nonlinear Dynamics, v. 92, n. 3, p. 1287-1297, 2018.
1573-269X
0924-090X
10.1007/s11071-018-4125-1
2-s2.0-85042069964
2-s2.0-85042069964.pdf
3757225669056317
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Dynamics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1287-1297
application/pdf
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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