Generalized hopf bifurcation in a frequency domain formulation

Autores
Torresi, Ana María Luján; Calandrini, Guillermo Luis; Bonfili, Paola Andrea; Moiola, Jorge Luis
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The multiplicity problem of limit cycles arising from a weak focus is addressed. The proposed methodology is a combination of the frequency domain method to handle some degenerate Hopf bifurcations with the powerful tools of the singularity theory. The frequency domain approach uses the harmonic balance method to study the existence of periodic solutions. On the other hand, the singularity theory provides the conditions and formulas for the classification problem of the unfolding of the singularity in terms of the distinguished and auxiliary parameters. A classical example introduced by Bautin is shown in which the multiplicity of limit cycles is recovered by using this type of hybrid methodology and standard software in the continuation of periodic solutions (LOCBIF and XPPAUT). For small amplitude limit cycles, the proposed methodology gives accurate results. © 2012 World Scientific Publishing Company.
Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Calandrini, Guillermo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
Fil: Bonfili, Paola Andrea. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
Materia
Frequency Domain
Harmonic Balance Method
Hopf Bifurcation
Limit Cycles
Singularity Theory
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:11336/62144
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/62144
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Generalized hopf bifurcation in a frequency domain formulationTorresi, Ana María LujánCalandrini, Guillermo LuisBonfili, Paola AndreaMoiola, Jorge LuisFrequency DomainHarmonic Balance MethodHopf BifurcationLimit CyclesSingularity Theoryhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2The multiplicity problem of limit cycles arising from a weak focus is addressed. The proposed methodology is a combination of the frequency domain method to handle some degenerate Hopf bifurcations with the powerful tools of the singularity theory. The frequency domain approach uses the harmonic balance method to study the existence of periodic solutions. On the other hand, the singularity theory provides the conditions and formulas for the classification problem of the unfolding of the singularity in terms of the distinguished and auxiliary parameters. A classical example introduced by Bautin is shown in which the multiplicity of limit cycles is recovered by using this type of hybrid methodology and standard software in the continuation of periodic solutions (LOCBIF and XPPAUT). For small amplitude limit cycles, the proposed methodology gives accurate results. © 2012 World Scientific Publishing Company.Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Calandrini, Guillermo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; ArgentinaFil: Bonfili, Paola Andrea. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; ArgentinaWorld Scientific2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/62144Torresi, Ana María Luján; Calandrini, Guillermo Luis; Bonfili, Paola Andrea; Moiola, Jorge Luis; Generalized hopf bifurcation in a frequency domain formulation; World Scientific; International Journal Of Bifurcation And Chaos; 22; 8; 8-2012; 1-160218-1274CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127412501970info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218127412501970info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:49:55Zoai:ri.conicet.gov.ar:11336/62144instacron: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 09:49:55.667CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Generalized hopf bifurcation in a frequency domain formulation
title Generalized hopf bifurcation in a frequency domain formulation
spellingShingle Generalized hopf bifurcation in a frequency domain formulation
Torresi, Ana María Luján
Frequency Domain
Harmonic Balance Method
Hopf Bifurcation
Limit Cycles
Singularity Theory
title_short Generalized hopf bifurcation in a frequency domain formulation
title_full Generalized hopf bifurcation in a frequency domain formulation
title_fullStr Generalized hopf bifurcation in a frequency domain formulation
title_full_unstemmed Generalized hopf bifurcation in a frequency domain formulation
title_sort Generalized hopf bifurcation in a frequency domain formulation
dc.creator.none.fl_str_mv Torresi, Ana María Luján
Calandrini, Guillermo Luis
Bonfili, Paola Andrea
Moiola, Jorge Luis
author Torresi, Ana María Luján
author_facet Torresi, Ana María Luján
Calandrini, Guillermo Luis
Bonfili, Paola Andrea
Moiola, Jorge Luis
author_role author
author2 Calandrini, Guillermo Luis
Bonfili, Paola Andrea
Moiola, Jorge Luis
author2_role author
author
author
dc.subject.none.fl_str_mv Frequency Domain
Harmonic Balance Method
Hopf Bifurcation
Limit Cycles
Singularity Theory
topic Frequency Domain
Harmonic Balance Method
Hopf Bifurcation
Limit Cycles
Singularity Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The multiplicity problem of limit cycles arising from a weak focus is addressed. The proposed methodology is a combination of the frequency domain method to handle some degenerate Hopf bifurcations with the powerful tools of the singularity theory. The frequency domain approach uses the harmonic balance method to study the existence of periodic solutions. On the other hand, the singularity theory provides the conditions and formulas for the classification problem of the unfolding of the singularity in terms of the distinguished and auxiliary parameters. A classical example introduced by Bautin is shown in which the multiplicity of limit cycles is recovered by using this type of hybrid methodology and standard software in the continuation of periodic solutions (LOCBIF and XPPAUT). For small amplitude limit cycles, the proposed methodology gives accurate results. © 2012 World Scientific Publishing Company.
Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Calandrini, Guillermo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
Fil: Bonfili, Paola Andrea. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
description The multiplicity problem of limit cycles arising from a weak focus is addressed. The proposed methodology is a combination of the frequency domain method to handle some degenerate Hopf bifurcations with the powerful tools of the singularity theory. The frequency domain approach uses the harmonic balance method to study the existence of periodic solutions. On the other hand, the singularity theory provides the conditions and formulas for the classification problem of the unfolding of the singularity in terms of the distinguished and auxiliary parameters. A classical example introduced by Bautin is shown in which the multiplicity of limit cycles is recovered by using this type of hybrid methodology and standard software in the continuation of periodic solutions (LOCBIF and XPPAUT). For small amplitude limit cycles, the proposed methodology gives accurate results. © 2012 World Scientific Publishing Company.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
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/11336/62144
Torresi, Ana María Luján; Calandrini, Guillermo Luis; Bonfili, Paola Andrea; Moiola, Jorge Luis; Generalized hopf bifurcation in a frequency domain formulation; World Scientific; International Journal Of Bifurcation And Chaos; 22; 8; 8-2012; 1-16
0218-1274
CONICET Digital
CONICET
url http://hdl.handle.net/11336/62144
identifier_str_mv Torresi, Ana María Luján; Calandrini, Guillermo Luis; Bonfili, Paola Andrea; Moiola, Jorge Luis; Generalized hopf bifurcation in a frequency domain formulation; World Scientific; International Journal Of Bifurcation And Chaos; 22; 8; 8-2012; 1-16
0218-1274
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127412501970
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218127412501970
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 World Scientific
publisher.none.fl_str_mv World Scientific
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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