Double Hopf bifurcation analysis using frequency domain methods

Autores
Itovich, Griselda Rut; Moiola, Jorge Luis
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The dynamic behavior close to a non-resonant double Hopf bifurcation is analyzed via a frequency-domain technique. Approximate expressions of the periodic solutions are computed using the higher order harmonic balance method while their accuracy and stability have been evaluated through the calculation of the multipliers of the monodromy matrix. Furthermore, the detection of secondary Hopf or torus bifurcations (Neimark–Sacker bifurcation for maps) close to the analyzed singularity has been obtained for a coupled electrical oscillatory circuit. Then, quasi-periodic solutions are likely to exist in certain regions of the parameter space. Extending this analysis to the unfolding of the 1:1 resonant double Hopf bifurcation, cyclic fold and torus bifurcations have also been detected in a controlled oscillatory coupled electrical circuit. The comparison of the results obtained with the suggested technique, and with continuation software packages, has been included.
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
HARMONIC BALANCE
LIMIT CYCLES
NEIMARK-SACKER 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:11336/104691
Acceder
id CONICETDig_59ea8c7bbd2ca8d2ba6d5afb9818004e
oai_identifier_str oai:ri.conicet.gov.ar:11336/104691
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Double Hopf bifurcation analysis using frequency domain methodsItovich, Griselda RutMoiola, Jorge LuisDOUBLE HOPF BIFURCATIONHARMONIC BALANCELIMIT CYCLESNEIMARK-SACKER BIFURCATIONhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2The dynamic behavior close to a non-resonant double Hopf bifurcation is analyzed via a frequency-domain technique. Approximate expressions of the periodic solutions are computed using the higher order harmonic balance method while their accuracy and stability have been evaluated through the calculation of the multipliers of the monodromy matrix. Furthermore, the detection of secondary Hopf or torus bifurcations (Neimark–Sacker bifurcation for maps) close to the analyzed singularity has been obtained for a coupled electrical oscillatory circuit. Then, quasi-periodic solutions are likely to exist in certain regions of the parameter space. Extending this analysis to the unfolding of the 1:1 resonant double Hopf bifurcation, cyclic fold and torus bifurcations have also been detected in a controlled oscillatory coupled electrical circuit. The comparison of the results obtained with the suggested technique, and with continuation software packages, has been included.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"; ArgentinaSpringer2005-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/104691Itovich, Griselda Rut; Moiola, Jorge Luis; Double Hopf bifurcation analysis using frequency domain methods; Springer ; Nonlinear Dynamics; 39; 2-2005; 235-2580924-090X1573-269XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11071-005-3543-zinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11071-005-3543-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:13:37Zoai:ri.conicet.gov.ar:11336/104691instacron: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:34982025-09-10 13:13:37.735CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Double Hopf bifurcation analysis using frequency domain methods
title Double Hopf bifurcation analysis using frequency domain methods
spellingShingle Double Hopf bifurcation analysis using frequency domain methods
Itovich, Griselda Rut
DOUBLE HOPF BIFURCATION
HARMONIC BALANCE
LIMIT CYCLES
NEIMARK-SACKER BIFURCATION
title_short Double Hopf bifurcation analysis using frequency domain methods
title_full Double Hopf bifurcation analysis using frequency domain methods
title_fullStr Double Hopf bifurcation analysis using frequency domain methods
title_full_unstemmed Double Hopf bifurcation analysis using frequency domain methods
title_sort Double Hopf bifurcation analysis using frequency domain methods
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
HARMONIC BALANCE
LIMIT CYCLES
NEIMARK-SACKER BIFURCATION
topic DOUBLE HOPF BIFURCATION
HARMONIC BALANCE
LIMIT CYCLES
NEIMARK-SACKER 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 The dynamic behavior close to a non-resonant double Hopf bifurcation is analyzed via a frequency-domain technique. Approximate expressions of the periodic solutions are computed using the higher order harmonic balance method while their accuracy and stability have been evaluated through the calculation of the multipliers of the monodromy matrix. Furthermore, the detection of secondary Hopf or torus bifurcations (Neimark–Sacker bifurcation for maps) close to the analyzed singularity has been obtained for a coupled electrical oscillatory circuit. Then, quasi-periodic solutions are likely to exist in certain regions of the parameter space. Extending this analysis to the unfolding of the 1:1 resonant double Hopf bifurcation, cyclic fold and torus bifurcations have also been detected in a controlled oscillatory coupled electrical circuit. The comparison of the results obtained with the suggested technique, and with continuation software packages, has been included.
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 dynamic behavior close to a non-resonant double Hopf bifurcation is analyzed via a frequency-domain technique. Approximate expressions of the periodic solutions are computed using the higher order harmonic balance method while their accuracy and stability have been evaluated through the calculation of the multipliers of the monodromy matrix. Furthermore, the detection of secondary Hopf or torus bifurcations (Neimark–Sacker bifurcation for maps) close to the analyzed singularity has been obtained for a coupled electrical oscillatory circuit. Then, quasi-periodic solutions are likely to exist in certain regions of the parameter space. Extending this analysis to the unfolding of the 1:1 resonant double Hopf bifurcation, cyclic fold and torus bifurcations have also been detected in a controlled oscillatory coupled electrical circuit. The comparison of the results obtained with the suggested technique, and with continuation software packages, has been included.
publishDate 2005
dc.date.none.fl_str_mv 2005-02
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/11336/104691
Itovich, Griselda Rut; Moiola, Jorge Luis; Double Hopf bifurcation analysis using frequency domain methods; Springer ; Nonlinear Dynamics; 39; 2-2005; 235-258
0924-090X
1573-269X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/104691
identifier_str_mv Itovich, Griselda Rut; Moiola, Jorge Luis; Double Hopf bifurcation analysis using frequency domain methods; Springer ; Nonlinear Dynamics; 39; 2-2005; 235-258
0924-090X
1573-269X
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://link.springer.com/article/10.1007/s11071-005-3543-z
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11071-005-3543-z
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 Springer
publisher.none.fl_str_mv Springer
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_ 1842980721820434432
score 12.993085

Publicaciones similares