Detection of limit cycle bifurcations using harmonic balance methods

Autores
Robbio, Federico I.; Alonso, Diego; Moiola, Jorge Luis
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rössler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities.
Fil: Robbio, Federico I.. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Alonso, Diego. 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: 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
HARMONIC BALANCE
LIMIT CYCLE BIFURCATIONS
MONODROMY MATRIX
HOPF BIFURCATIONS
PERIOD-DOUBLING
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:11336/105316
Acceder
id CONICETDig_1e9257ab7967d278a201700bdaae763e
oai_identifier_str oai:ri.conicet.gov.ar:11336/105316
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Detection of limit cycle bifurcations using harmonic balance methodsRobbio, Federico I.Alonso, DiegoMoiola, Jorge LuisHARMONIC BALANCELIMIT CYCLE BIFURCATIONSMONODROMY MATRIXHOPF BIFURCATIONSPERIOD-DOUBLINGhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rössler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities.Fil: Robbio, Federico I.. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Alonso, Diego. 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: 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; ArgentinaWorld Scientific2004-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105316Robbio, Federico I.; Alonso, Diego; Moiola, Jorge Luis; Detection of limit cycle bifurcations using harmonic balance methods; World Scientific; International Journal Of Bifurcation And Chaos; 14; 10; 12-2004; 3647-36540218-12741793-6551CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218127404011491info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127404011491info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:03:42Zoai:ri.conicet.gov.ar:11336/105316instacron: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 10:03:42.428CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Detection of limit cycle bifurcations using harmonic balance methods
title Detection of limit cycle bifurcations using harmonic balance methods
spellingShingle Detection of limit cycle bifurcations using harmonic balance methods
Robbio, Federico I.
HARMONIC BALANCE
LIMIT CYCLE BIFURCATIONS
MONODROMY MATRIX
HOPF BIFURCATIONS
PERIOD-DOUBLING
title_short Detection of limit cycle bifurcations using harmonic balance methods
title_full Detection of limit cycle bifurcations using harmonic balance methods
title_fullStr Detection of limit cycle bifurcations using harmonic balance methods
title_full_unstemmed Detection of limit cycle bifurcations using harmonic balance methods
title_sort Detection of limit cycle bifurcations using harmonic balance methods
dc.creator.none.fl_str_mv Robbio, Federico I.
Alonso, Diego
Moiola, Jorge Luis
author Robbio, Federico I.
author_facet Robbio, Federico I.
Alonso, Diego
Moiola, Jorge Luis
author_role author
author2 Alonso, Diego
Moiola, Jorge Luis
author2_role author
author
dc.subject.none.fl_str_mv HARMONIC BALANCE
LIMIT CYCLE BIFURCATIONS
MONODROMY MATRIX
HOPF BIFURCATIONS
PERIOD-DOUBLING
topic HARMONIC BALANCE
LIMIT CYCLE BIFURCATIONS
MONODROMY MATRIX
HOPF BIFURCATIONS
PERIOD-DOUBLING
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rössler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities.
Fil: Robbio, Federico I.. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Alonso, Diego. 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: 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 In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rössler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities.
publishDate 2004
dc.date.none.fl_str_mv 2004-12
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/11336/105316
Robbio, Federico I.; Alonso, Diego; Moiola, Jorge Luis; Detection of limit cycle bifurcations using harmonic balance methods; World Scientific; International Journal Of Bifurcation And Chaos; 14; 10; 12-2004; 3647-3654
0218-1274
1793-6551
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105316
identifier_str_mv Robbio, Federico I.; Alonso, Diego; Moiola, Jorge Luis; Detection of limit cycle bifurcations using harmonic balance methods; World Scientific; International Journal Of Bifurcation And Chaos; 14; 10; 12-2004; 3647-3654
0218-1274
1793-6551
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.worldscientific.com/doi/abs/10.1142/S0218127404011491
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127404011491
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
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
_version_ 1844613855906365440
score 13.070432

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