A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions

Autores
Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, the dynamics of a coupled electric circuit is studied. Several bifurcation diagrams associated with the truncated normal form of the Hopf-Hopf bifurcation are presented. The bifurcation curves are obtained by numerical continuation methods. The existence of quasi-periodic solutions with two (2D torus) and three (3D torus) frequency components is shown. These, in certain way, are close (or have a tendency to end up) to chaotic motion. Furthermore, two fold-flip bifurcations are detected in the vicinity of the Hopf-Hopf bifurcation, and are classified correspondingly. The analysis is completed with time simulations, the continuation of several limit cycle bifurcations and the indication of resonance points.
Fil: Revel, Gustavo. 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: Alonso, Diego. 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: 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
BIFURCATIONS OF PERIODIC ORBITS
QUASIPERIODIC SOLUTIONS
DOUBLE HOPF BIFURCATION
FOLD-FLIP 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:11336/105450
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactionsRevel, GustavoAlonso, DiegoMoiola, Jorge LuisBIFURCATIONS OF PERIODIC ORBITSQUASIPERIODIC SOLUTIONSDOUBLE HOPF BIFURCATIONFOLD-FLIP BIFURCATIONhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this work, the dynamics of a coupled electric circuit is studied. Several bifurcation diagrams associated with the truncated normal form of the Hopf-Hopf bifurcation are presented. The bifurcation curves are obtained by numerical continuation methods. The existence of quasi-periodic solutions with two (2D torus) and three (3D torus) frequency components is shown. These, in certain way, are close (or have a tendency to end up) to chaotic motion. Furthermore, two fold-flip bifurcations are detected in the vicinity of the Hopf-Hopf bifurcation, and are classified correspondingly. The analysis is completed with time simulations, the continuation of several limit cycle bifurcations and the indication of resonance points.Fil: Revel, Gustavo. 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: Alonso, Diego. 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: 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 Scientific2008-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105450Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions; World Scientific; International Journal Of Bifurcation And Chaos; 18; 02; 12-2008; 481-4940218-12741793-6551CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0218127408020409info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127408020409info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:22:54Zoai:ri.conicet.gov.ar:11336/105450instacron: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 10:22:54.832CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
title A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
spellingShingle A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
Revel, Gustavo
BIFURCATIONS OF PERIODIC ORBITS
QUASIPERIODIC SOLUTIONS
DOUBLE HOPF BIFURCATION
FOLD-FLIP BIFURCATION
title_short A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
title_full A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
title_fullStr A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
title_full_unstemmed A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
title_sort A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions
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 BIFURCATIONS OF PERIODIC ORBITS
QUASIPERIODIC SOLUTIONS
DOUBLE HOPF BIFURCATION
FOLD-FLIP BIFURCATION
topic BIFURCATIONS OF PERIODIC ORBITS
QUASIPERIODIC SOLUTIONS
DOUBLE HOPF BIFURCATION
FOLD-FLIP 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 In this work, the dynamics of a coupled electric circuit is studied. Several bifurcation diagrams associated with the truncated normal form of the Hopf-Hopf bifurcation are presented. The bifurcation curves are obtained by numerical continuation methods. The existence of quasi-periodic solutions with two (2D torus) and three (3D torus) frequency components is shown. These, in certain way, are close (or have a tendency to end up) to chaotic motion. Furthermore, two fold-flip bifurcations are detected in the vicinity of the Hopf-Hopf bifurcation, and are classified correspondingly. The analysis is completed with time simulations, the continuation of several limit cycle bifurcations and the indication of resonance points.
Fil: Revel, Gustavo. 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: Alonso, Diego. 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: 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 In this work, the dynamics of a coupled electric circuit is studied. Several bifurcation diagrams associated with the truncated normal form of the Hopf-Hopf bifurcation are presented. The bifurcation curves are obtained by numerical continuation methods. The existence of quasi-periodic solutions with two (2D torus) and three (3D torus) frequency components is shown. These, in certain way, are close (or have a tendency to end up) to chaotic motion. Furthermore, two fold-flip bifurcations are detected in the vicinity of the Hopf-Hopf bifurcation, and are classified correspondingly. The analysis is completed with time simulations, the continuation of several limit cycle bifurcations and the indication of resonance points.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
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/11336/105450
Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions; World Scientific; International Journal Of Bifurcation And Chaos; 18; 02; 12-2008; 481-494
0218-1274
1793-6551
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105450
identifier_str_mv Revel, Gustavo; Alonso, Diego; Moiola, Jorge Luis; A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions; World Scientific; International Journal Of Bifurcation And Chaos; 18; 02; 12-2008; 481-494
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/10.1142/S0218127408020409
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127408020409
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
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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