On period doubling bifurcations of cycles and the harmonic balance method

Autores
Itovich, Griselda Rut; Moiola, Jorge Luis
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.
Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; Argentina
Fil: Moiola, Jorge Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Materia
Period-doubling
Bifurcation
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:11336/105138
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/105138
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On period doubling bifurcations of cycles and the harmonic balance methodItovich, Griselda RutMoiola, Jorge LuisPeriod-doublingBifurcationhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; ArgentinaFil: Moiola, Jorge Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaPergamon-Elsevier Science Ltd2006-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105138Itovich, Griselda Rut; Moiola, Jorge Luis; On period doubling bifurcations of cycles and the harmonic balance method; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 27; 3; 2-2006; 647-6650960-0779CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0960077905003929info:eu-repo/semantics/altIdentifier/doi/10.1016/j.chaos.2005.04.061info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:09:23Zoai:ri.conicet.gov.ar:11336/105138instacron: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 12:09:23.43CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On period doubling bifurcations of cycles and the harmonic balance method
title On period doubling bifurcations of cycles and the harmonic balance method
spellingShingle On period doubling bifurcations of cycles and the harmonic balance method
Itovich, Griselda Rut
Period-doubling
Bifurcation
title_short On period doubling bifurcations of cycles and the harmonic balance method
title_full On period doubling bifurcations of cycles and the harmonic balance method
title_fullStr On period doubling bifurcations of cycles and the harmonic balance method
title_full_unstemmed On period doubling bifurcations of cycles and the harmonic balance method
title_sort On period doubling bifurcations of cycles and the harmonic balance method
dc.creator.none.fl_str_mv Itovich, Griselda Rut
Moiola, Jorge Luis
author Itovich, Griselda Rut
author_facet Itovich, Griselda Rut
Moiola, Jorge Luis
author_role author
author2 Moiola, Jorge Luis
author2_role author
dc.subject.none.fl_str_mv Period-doubling
Bifurcation
topic Period-doubling
Bifurcation
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.
Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; Argentina
Fil: Moiola, Jorge Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
description This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.
publishDate 2006
dc.date.none.fl_str_mv 2006-02
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/11336/105138
Itovich, Griselda Rut; Moiola, Jorge Luis; On period doubling bifurcations of cycles and the harmonic balance method; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 27; 3; 2-2006; 647-665
0960-0779
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105138
identifier_str_mv Itovich, Griselda Rut; Moiola, Jorge Luis; On period doubling bifurcations of cycles and the harmonic balance method; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 27; 3; 2-2006; 647-665
0960-0779
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/abs/pii/S0960077905003929
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.chaos.2005.04.061
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 12.982451

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