On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | |
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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808129201338843136 |