Detecting period-doubling bifurcation: An approximate monodromy matrix approach

Autores
Berns, Daniel Walther; Moiola, Jorge Luis; Chen, Guanrong
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A quasi-analytical approach is developed for detecting period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order Harmonic Balance Approximations (HBAs) to compute the monodromy matrix, useful for the study of limit cycle bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this algorithm, along with a detailed approximation error analysis, without using numerical integration of the dynamical system. An example is given to illustrate the results.
Fil: Berns, Daniel Walther. Universidad Nacional de la Patagonia "San Juan Bosco"; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Chen, Guanrong. City University of Hong Kong; China
Materia
Period-doubling
Monodromy
Frequency
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:11336/104079
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Detecting period-doubling bifurcation: An approximate monodromy matrix approachBerns, Daniel WaltherMoiola, Jorge LuisChen, GuanrongPeriod-doublingMonodromyFrequencyhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2A quasi-analytical approach is developed for detecting period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order Harmonic Balance Approximations (HBAs) to compute the monodromy matrix, useful for the study of limit cycle bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this algorithm, along with a detailed approximation error analysis, without using numerical integration of the dynamical system. An example is given to illustrate the results.Fil: Berns, Daniel Walther. Universidad Nacional de la Patagonia "San Juan Bosco"; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Chen, Guanrong. City University of Hong Kong; ChinaPergamon-Elsevier Science Ltd2001-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/104079Berns, Daniel Walther; Moiola, Jorge Luis; Chen, Guanrong; Detecting period-doubling bifurcation: An approximate monodromy matrix approach; Pergamon-Elsevier Science Ltd; Automatica; 37; 11; 11-2001; 1787-17950005-1098CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0005109801001315info:eu-repo/semantics/altIdentifier/doi/10.1016/S0005-1098(01)00131-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:44:57Zoai:ri.conicet.gov.ar:11336/104079instacron: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:34982025-09-29 09:44:57.788CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Detecting period-doubling bifurcation: An approximate monodromy matrix approach
title Detecting period-doubling bifurcation: An approximate monodromy matrix approach
spellingShingle Detecting period-doubling bifurcation: An approximate monodromy matrix approach
Berns, Daniel Walther
Period-doubling
Monodromy
Frequency
title_short Detecting period-doubling bifurcation: An approximate monodromy matrix approach
title_full Detecting period-doubling bifurcation: An approximate monodromy matrix approach
title_fullStr Detecting period-doubling bifurcation: An approximate monodromy matrix approach
title_full_unstemmed Detecting period-doubling bifurcation: An approximate monodromy matrix approach
title_sort Detecting period-doubling bifurcation: An approximate monodromy matrix approach
dc.creator.none.fl_str_mv Berns, Daniel Walther
Moiola, Jorge Luis
Chen, Guanrong
author Berns, Daniel Walther
author_facet Berns, Daniel Walther
Moiola, Jorge Luis
Chen, Guanrong
author_role author
author2 Moiola, Jorge Luis
Chen, Guanrong
author2_role author
author
dc.subject.none.fl_str_mv Period-doubling
Monodromy
Frequency
topic Period-doubling
Monodromy
Frequency
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv A quasi-analytical approach is developed for detecting period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order Harmonic Balance Approximations (HBAs) to compute the monodromy matrix, useful for the study of limit cycle bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this algorithm, along with a detailed approximation error analysis, without using numerical integration of the dynamical system. An example is given to illustrate the results.
Fil: Berns, Daniel Walther. Universidad Nacional de la Patagonia "San Juan Bosco"; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Chen, Guanrong. City University of Hong Kong; China
description A quasi-analytical approach is developed for detecting period-doubling bifurcation emerging near a Hopf bifurcation point. The new algorithm employs higher-order Harmonic Balance Approximations (HBAs) to compute the monodromy matrix, useful for the study of limit cycle bifurcations. Prediction of the period-doubling bifurcation is accomplished very accurately by using this algorithm, along with a detailed approximation error analysis, without using numerical integration of the dynamical system. An example is given to illustrate the results.
publishDate 2001
dc.date.none.fl_str_mv 2001-11
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/11336/104079
Berns, Daniel Walther; Moiola, Jorge Luis; Chen, Guanrong; Detecting period-doubling bifurcation: An approximate monodromy matrix approach; Pergamon-Elsevier Science Ltd; Automatica; 37; 11; 11-2001; 1787-1795
0005-1098
CONICET Digital
CONICET
url http://hdl.handle.net/11336/104079
identifier_str_mv Berns, Daniel Walther; Moiola, Jorge Luis; Chen, Guanrong; Detecting period-doubling bifurcation: An approximate monodromy matrix approach; Pergamon-Elsevier Science Ltd; Automatica; 37; 11; 11-2001; 1787-1795
0005-1098
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0005109801001315
info:eu-repo/semantics/altIdentifier/doi/10.1016/S0005-1098(01)00131-5
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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 13.070432

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