Non-resonant double Hopf bifurcations: The complex case

Autores
Itovich, Griselda Rut; Moiola, Jorge Luis
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The analysis of the unfolding of a non-resonant double Hopf singularity is considered using the frequency domain and the normal form methodologies. A higher-order harmonic balance and the evaluation of Floquet multipliers are used to obtain accurate approximations of the limit cycles and its local bifurcations. This type of hybrid methodology using harmonic balance and normal forms gives a complementary view in the vicinity of the singularity. More specifically, some of the bifurcation curves arising in the unfolding of the double Hopf bifurcation are computed with great accuracy using the harmonic balance method compared to the classical normal form. However, this last method is able to predict the appearance of complex quasiperiodic behavior such as three-dimensional (3D) torus. Numerical simulations corroborate this observation.
Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; 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
Double Hopf bifurcation
Frequency domain methods
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:11336/105306
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/105306
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Non-resonant double Hopf bifurcations: The complex caseItovich, Griselda RutMoiola, Jorge LuisDouble Hopf bifurcationFrequency domain methodshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The analysis of the unfolding of a non-resonant double Hopf singularity is considered using the frequency domain and the normal form methodologies. A higher-order harmonic balance and the evaluation of Floquet multipliers are used to obtain accurate approximations of the limit cycles and its local bifurcations. This type of hybrid methodology using harmonic balance and normal forms gives a complementary view in the vicinity of the singularity. More specifically, some of the bifurcation curves arising in the unfolding of the double Hopf bifurcation are computed with great accuracy using the harmonic balance method compared to the classical normal form. However, this last method is able to predict the appearance of complex quasiperiodic behavior such as three-dimensional (3D) torus. Numerical simulations corroborate this observation.Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; 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"; ArgentinaAcademic Press Ltd - Elsevier Science Ltd2009-04-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105306Itovich, Griselda Rut; Moiola, Jorge Luis; Non-resonant double Hopf bifurcations: The complex case; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 322; 1-2; 24-4-2009; 358-3800022-460XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022460X0800922Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsv.2008.11.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T09:09:40Zoai:ri.conicet.gov.ar:11336/105306instacron: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:34982025-11-26 09:09:41.056CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Non-resonant double Hopf bifurcations: The complex case
title Non-resonant double Hopf bifurcations: The complex case
spellingShingle Non-resonant double Hopf bifurcations: The complex case
Itovich, Griselda Rut
Double Hopf bifurcation
Frequency domain methods
title_short Non-resonant double Hopf bifurcations: The complex case
title_full Non-resonant double Hopf bifurcations: The complex case
title_fullStr Non-resonant double Hopf bifurcations: The complex case
title_full_unstemmed Non-resonant double Hopf bifurcations: The complex case
title_sort Non-resonant double Hopf bifurcations: The complex case
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 Double Hopf bifurcation
Frequency domain methods
topic Double Hopf bifurcation
Frequency domain methods
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The analysis of the unfolding of a non-resonant double Hopf singularity is considered using the frequency domain and the normal form methodologies. A higher-order harmonic balance and the evaluation of Floquet multipliers are used to obtain accurate approximations of the limit cycles and its local bifurcations. This type of hybrid methodology using harmonic balance and normal forms gives a complementary view in the vicinity of the singularity. More specifically, some of the bifurcation curves arising in the unfolding of the double Hopf bifurcation are computed with great accuracy using the harmonic balance method compared to the classical normal form. However, this last method is able to predict the appearance of complex quasiperiodic behavior such as three-dimensional (3D) torus. Numerical simulations corroborate this observation.
Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; 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 analysis of the unfolding of a non-resonant double Hopf singularity is considered using the frequency domain and the normal form methodologies. A higher-order harmonic balance and the evaluation of Floquet multipliers are used to obtain accurate approximations of the limit cycles and its local bifurcations. This type of hybrid methodology using harmonic balance and normal forms gives a complementary view in the vicinity of the singularity. More specifically, some of the bifurcation curves arising in the unfolding of the double Hopf bifurcation are computed with great accuracy using the harmonic balance method compared to the classical normal form. However, this last method is able to predict the appearance of complex quasiperiodic behavior such as three-dimensional (3D) torus. Numerical simulations corroborate this observation.
publishDate 2009
dc.date.none.fl_str_mv 2009-04-24
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/11336/105306
Itovich, Griselda Rut; Moiola, Jorge Luis; Non-resonant double Hopf bifurcations: The complex case; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 322; 1-2; 24-4-2009; 358-380
0022-460X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105306
identifier_str_mv Itovich, Griselda Rut; Moiola, Jorge Luis; Non-resonant double Hopf bifurcations: The complex case; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 322; 1-2; 24-4-2009; 358-380
0022-460X
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/S0022460X0800922X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsv.2008.11.005
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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
publisher.none.fl_str_mv Academic Press Ltd - 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
_version_ 1849873651097141248
score 13.011256

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