High order analysis of the limit cycle of the van der Pol oscillator

Autores
Amore, Paolo; Boyd, John P.; Fernández, Francisco Marcelo
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the amplitude to order 859. Hermite-Padé approximants have been used to extract the location of the branch cut of the series with unprecedented accuracy (100 digits). Both series have then been resummed using an approach based on Padé approximants, where the exact asymptotic behaviors of the period and the amplitude are taken into account. Our results improve drastically all previous results obtained on this subject.
Fil: Amore, Paolo. Universidad de Colima; México
Fil: Boyd, John P.. University of Michigan; Estados Unidos
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Materia
VAN DER POL
PERTURBATION THEORY
LARGE ORDER
BRANCH CUT
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/99951
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/99951
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network_name_str CONICET Digital (CONICET)
spelling High order analysis of the limit cycle of the van der Pol oscillatorAmore, PaoloBoyd, John P.Fernández, Francisco MarceloVAN DER POLPERTURBATION THEORYLARGE ORDERBRANCH CUThttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the amplitude to order 859. Hermite-Padé approximants have been used to extract the location of the branch cut of the series with unprecedented accuracy (100 digits). Both series have then been resummed using an approach based on Padé approximants, where the exact asymptotic behaviors of the period and the amplitude are taken into account. Our results improve drastically all previous results obtained on this subject.Fil: Amore, Paolo. Universidad de Colima; MéxicoFil: Boyd, John P.. University of Michigan; Estados UnidosFil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaAmerican Institute of Physics2018-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/99951Amore, Paolo; Boyd, John P.; Fernández, Francisco Marcelo; High order analysis of the limit cycle of the van der Pol oscillator; American Institute of Physics; Journal of Mathematical Physics; 59; 1; 1-2018; 1-11; 0127020022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.5016961info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.5016961info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1711.09978info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:18:22Zoai:ri.conicet.gov.ar:11336/99951instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:18:22.525CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv High order analysis of the limit cycle of the van der Pol oscillator
title High order analysis of the limit cycle of the van der Pol oscillator
spellingShingle High order analysis of the limit cycle of the van der Pol oscillator
Amore, Paolo
VAN DER POL
PERTURBATION THEORY
LARGE ORDER
BRANCH CUT
title_short High order analysis of the limit cycle of the van der Pol oscillator
title_full High order analysis of the limit cycle of the van der Pol oscillator
title_fullStr High order analysis of the limit cycle of the van der Pol oscillator
title_full_unstemmed High order analysis of the limit cycle of the van der Pol oscillator
title_sort High order analysis of the limit cycle of the van der Pol oscillator
dc.creator.none.fl_str_mv Amore, Paolo
Boyd, John P.
Fernández, Francisco Marcelo
author Amore, Paolo
author_facet Amore, Paolo
Boyd, John P.
Fernández, Francisco Marcelo
author_role author
author2 Boyd, John P.
Fernández, Francisco Marcelo
author2_role author
author
dc.subject.none.fl_str_mv VAN DER POL
PERTURBATION THEORY
LARGE ORDER
BRANCH CUT
topic VAN DER POL
PERTURBATION THEORY
LARGE ORDER
BRANCH CUT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.4
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the amplitude to order 859. Hermite-Padé approximants have been used to extract the location of the branch cut of the series with unprecedented accuracy (100 digits). Both series have then been resummed using an approach based on Padé approximants, where the exact asymptotic behaviors of the period and the amplitude are taken into account. Our results improve drastically all previous results obtained on this subject.
Fil: Amore, Paolo. Universidad de Colima; México
Fil: Boyd, John P.. University of Michigan; Estados Unidos
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
description We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the amplitude to order 859. Hermite-Padé approximants have been used to extract the location of the branch cut of the series with unprecedented accuracy (100 digits). Both series have then been resummed using an approach based on Padé approximants, where the exact asymptotic behaviors of the period and the amplitude are taken into account. Our results improve drastically all previous results obtained on this subject.
publishDate 2018
dc.date.none.fl_str_mv 2018-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/99951
Amore, Paolo; Boyd, John P.; Fernández, Francisco Marcelo; High order analysis of the limit cycle of the van der Pol oscillator; American Institute of Physics; Journal of Mathematical Physics; 59; 1; 1-2018; 1-11; 012702
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/99951
identifier_str_mv Amore, Paolo; Boyd, John P.; Fernández, Francisco Marcelo; High order analysis of the limit cycle of the van der Pol oscillator; American Institute of Physics; Journal of Mathematical Physics; 59; 1; 1-2018; 1-11; 012702
0022-2488
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/1.5016961
info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.5016961
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1711.09978
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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