Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation

Autores
Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, a numerical semi-global analysis of the dynamics near a 1:2 resonant Hopf-Hopf bifurcation on a four-dimensional mathematical model of a simple nonlinear oscillator is performed. The 1:2 resonant Hopf-Hopf bifurcation is a codimension-three singularity denoted by two pairs of purely imaginary eigenvalues with frequency ratio 1:2. A structure involving 1:1 and 1:2 resonant Neimark-Sacker bifurcations is clearly identified. Both resonances are coupled by lower-codimension singularities, such as generalized Hopf and period doubling, cusp points, and cyclic fold curves. A three-parameter semiglobal analysis is performed and some of the codimension-two singularities unfolded by the 1:2 resonant Hopf-Hopf bifurcation are identified. Several codimension-three points are also detected. The obtained results can be useful for further theoretical analysis of the corresponding normal form.
Fil: Revel, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación En Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
Fil: Alonso, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
Materia
Hopf-Hopf Bifurcation
Strong Resonances
Nonlinear Oscillators
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/11773
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcationRevel, GustavoAlonso, DiegoMoiola, Jorge LuisHopf-Hopf BifurcationStrong ResonancesNonlinear Oscillatorshttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this paper, a numerical semi-global analysis of the dynamics near a 1:2 resonant Hopf-Hopf bifurcation on a four-dimensional mathematical model of a simple nonlinear oscillator is performed. The 1:2 resonant Hopf-Hopf bifurcation is a codimension-three singularity denoted by two pairs of purely imaginary eigenvalues with frequency ratio 1:2. A structure involving 1:1 and 1:2 resonant Neimark-Sacker bifurcations is clearly identified. Both resonances are coupled by lower-codimension singularities, such as generalized Hopf and period doubling, cusp points, and cyclic fold curves. A three-parameter semiglobal analysis is performed and some of the codimension-two singularities unfolded by the 1:2 resonant Hopf-Hopf bifurcation are identified. Several codimension-three points are also detected. The obtained results can be useful for further theoretical analysis of the corresponding normal form.Fil: Revel, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación En Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; ArgentinaFil: Alonso, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; ArgentinaElsevier Science2013-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/11773Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation; Elsevier Science; Physica D - Nonlinear Phenomena; 247; 1; 3-2013; 40-530167-2789enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0167278912003119info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2012.12.007info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:50:34Zoai:ri.conicet.gov.ar:11336/11773instacron: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:34982025-10-29 12:50:34.448CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
title Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
spellingShingle Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
Revel, Gustavo
Hopf-Hopf Bifurcation
Strong Resonances
Nonlinear Oscillators
title_short Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
title_full Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
title_fullStr Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
title_full_unstemmed Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
title_sort Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation
dc.creator.none.fl_str_mv Revel, Gustavo
Alonso, Diego
Moiola, Jorge Luis
author Revel, Gustavo
author_facet Revel, Gustavo
Alonso, Diego
Moiola, Jorge Luis
author_role author
author2 Alonso, Diego
Moiola, Jorge Luis
author2_role author
author
dc.subject.none.fl_str_mv Hopf-Hopf Bifurcation
Strong Resonances
Nonlinear Oscillators
topic Hopf-Hopf Bifurcation
Strong Resonances
Nonlinear Oscillators
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, a numerical semi-global analysis of the dynamics near a 1:2 resonant Hopf-Hopf bifurcation on a four-dimensional mathematical model of a simple nonlinear oscillator is performed. The 1:2 resonant Hopf-Hopf bifurcation is a codimension-three singularity denoted by two pairs of purely imaginary eigenvalues with frequency ratio 1:2. A structure involving 1:1 and 1:2 resonant Neimark-Sacker bifurcations is clearly identified. Both resonances are coupled by lower-codimension singularities, such as generalized Hopf and period doubling, cusp points, and cyclic fold curves. A three-parameter semiglobal analysis is performed and some of the codimension-two singularities unfolded by the 1:2 resonant Hopf-Hopf bifurcation are identified. Several codimension-three points are also detected. The obtained results can be useful for further theoretical analysis of the corresponding normal form.
Fil: Revel, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación En Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
Fil: Alonso, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
description In this paper, a numerical semi-global analysis of the dynamics near a 1:2 resonant Hopf-Hopf bifurcation on a four-dimensional mathematical model of a simple nonlinear oscillator is performed. The 1:2 resonant Hopf-Hopf bifurcation is a codimension-three singularity denoted by two pairs of purely imaginary eigenvalues with frequency ratio 1:2. A structure involving 1:1 and 1:2 resonant Neimark-Sacker bifurcations is clearly identified. Both resonances are coupled by lower-codimension singularities, such as generalized Hopf and period doubling, cusp points, and cyclic fold curves. A three-parameter semiglobal analysis is performed and some of the codimension-two singularities unfolded by the 1:2 resonant Hopf-Hopf bifurcation are identified. Several codimension-three points are also detected. The obtained results can be useful for further theoretical analysis of the corresponding normal form.
publishDate 2013
dc.date.none.fl_str_mv 2013-03
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/11336/11773
Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation; Elsevier Science; Physica D - Nonlinear Phenomena; 247; 1; 3-2013; 40-53
0167-2789
url http://hdl.handle.net/11336/11773
identifier_str_mv Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; Numerical semi-global analysis of a 1:2 resonant Hopf-Hopf bifurcation; Elsevier Science; Physica D - Nonlinear Phenomena; 247; 1; 3-2013; 40-53
0167-2789
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0167278912003119
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2012.12.007
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 13.10058

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