Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/00207160.2015.1046847 http://hdl.handle.net/11449/171875 |
Resumo: | In this paper, some aspects on the periodic solutions of the extended Duffing–Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing–Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques. |
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Repositório Institucional da UNESP |
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Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillatoraveraging theoryextended Duffing–Van der Pol oscillatornon-autonomous systemsperiodic solutionIn this paper, some aspects on the periodic solutions of the extended Duffing–Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing–Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques.Agència de Gestió d’Ajuts Universitaris i de RecercaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Departament de Matemàtiques Universitat Autònoma de BarcelonaDepartament de Matemática IBILCE UNESP, Rua Cristovao Colombo 2265, Jardim Nazareth, CEP 15.054–00Departament de Matemática IBILCE UNESP, Rua Cristovao Colombo 2265, Jardim Nazareth, CEP 15.054–00Agència de Gestió d’Ajuts Universitaris i de Recerca: 2014SGR568CAPES: 88881.030454/2013-01Universitat Autònoma de BarcelonaUniversidade Estadual Paulista (Unesp)Euzébio, Rodrigo D. [UNESP]Llibre, Jaume2018-12-11T16:57:32Z2018-12-11T16:57:32Z2016-08-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1358-1382application/pdfhttp://dx.doi.org/10.1080/00207160.2015.1046847International Journal of Computer Mathematics, v. 93, n. 8, p. 1358-1382, 2016.1029-02650020-7160http://hdl.handle.net/11449/17187510.1080/00207160.2015.10468472-s2.0-849307070502-s2.0-84930707050.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Computer Mathematics0,456info:eu-repo/semantics/openAccess2024-01-11T06:25:19Zoai:repositorio.unesp.br:11449/171875Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-05-23T20:22:54.299320Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
title |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
spellingShingle |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator Euzébio, Rodrigo D. [UNESP] averaging theory extended Duffing–Van der Pol oscillator non-autonomous systems periodic solution |
title_short |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
title_full |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
title_fullStr |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
title_full_unstemmed |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
title_sort |
Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator |
author |
Euzébio, Rodrigo D. [UNESP] |
author_facet |
Euzébio, Rodrigo D. [UNESP] Llibre, Jaume |
author_role |
author |
author2 |
Llibre, Jaume |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universitat Autònoma de Barcelona Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Euzébio, Rodrigo D. [UNESP] Llibre, Jaume |
dc.subject.por.fl_str_mv |
averaging theory extended Duffing–Van der Pol oscillator non-autonomous systems periodic solution |
topic |
averaging theory extended Duffing–Van der Pol oscillator non-autonomous systems periodic solution |
description |
In this paper, some aspects on the periodic solutions of the extended Duffing–Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing–Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-08-02 2018-12-11T16:57:32Z 2018-12-11T16:57:32Z |
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/10.1080/00207160.2015.1046847 International Journal of Computer Mathematics, v. 93, n. 8, p. 1358-1382, 2016. 1029-0265 0020-7160 http://hdl.handle.net/11449/171875 10.1080/00207160.2015.1046847 2-s2.0-84930707050 2-s2.0-84930707050.pdf |
url |
http://dx.doi.org/10.1080/00207160.2015.1046847 http://hdl.handle.net/11449/171875 |
identifier_str_mv |
International Journal of Computer Mathematics, v. 93, n. 8, p. 1358-1382, 2016. 1029-0265 0020-7160 10.1080/00207160.2015.1046847 2-s2.0-84930707050 2-s2.0-84930707050.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Computer Mathematics 0,456 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1358-1382 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_ |
1803045666909323264 |