Analysis of the Van der Pol oscillator containing derivatives of fractional order

Detalhes bibliográficos
Autor(a) principal: Barbosa, Ramiro S.
Data de Publicação: 2007
Outros Autores: Machado, J. A. Tenreiro, Vinagre, B. M., Calderón, A. J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/4576
Resumo: In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.
id RCAP_6cd9bd114e9e2410664a3bd60f5aa8c1
oai_identifier_str oai:recipp.ipp.pt:10400.22/4576
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Analysis of the Van der Pol oscillator containing derivatives of fractional orderFractional calculusVan der Pol oscillatorNonlinear oscillatorsFractional order operatorsIn this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.SAGE PublicationsRepositório Científico do Instituto Politécnico do PortoBarbosa, Ramiro S.Machado, J. A. TenreiroVinagre, B. M.Calderón, A. J.2014-06-25T11:14:29Z20072007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/4576eng1077-546310.1177/1077546307077463info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T12:44:41Zoai:recipp.ipp.pt:10400.22/4576Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:25:25.184368Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Analysis of the Van der Pol oscillator containing derivatives of fractional order
title Analysis of the Van der Pol oscillator containing derivatives of fractional order
spellingShingle Analysis of the Van der Pol oscillator containing derivatives of fractional order
Barbosa, Ramiro S.
Fractional calculus
Van der Pol oscillator
Nonlinear oscillators
Fractional order operators
title_short Analysis of the Van der Pol oscillator containing derivatives of fractional order
title_full Analysis of the Van der Pol oscillator containing derivatives of fractional order
title_fullStr Analysis of the Van der Pol oscillator containing derivatives of fractional order
title_full_unstemmed Analysis of the Van der Pol oscillator containing derivatives of fractional order
title_sort Analysis of the Van der Pol oscillator containing derivatives of fractional order
author Barbosa, Ramiro S.
author_facet Barbosa, Ramiro S.
Machado, J. A. Tenreiro
Vinagre, B. M.
Calderón, A. J.
author_role author
author2 Machado, J. A. Tenreiro
Vinagre, B. M.
Calderón, A. J.
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Barbosa, Ramiro S.
Machado, J. A. Tenreiro
Vinagre, B. M.
Calderón, A. J.
dc.subject.por.fl_str_mv Fractional calculus
Van der Pol oscillator
Nonlinear oscillators
Fractional order operators
topic Fractional calculus
Van der Pol oscillator
Nonlinear oscillators
Fractional order operators
description In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-01-01T00:00:00Z
2014-06-25T11:14:29Z
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://hdl.handle.net/10400.22/4576
url http://hdl.handle.net/10400.22/4576
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1077-5463
10.1177/1077546307077463
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv SAGE Publications
publisher.none.fl_str_mv SAGE Publications
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799131347693862912

Registros relacionados