Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback

Autores
Gentile, Franco Sebastián; Itovich, Griselda Rut; Moiola, Jorge Luis
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, the dynamics of an oscillator with delayed feedback is analyzed. It is found that for certain values of the parameters, the system exhibits a phenomenon known as double Hopf bifurcation with 1:2 resonance. This singularity provokes the interaction between two oscillatory solutions, one of frequency ω and the other with frequency 2 ω. By using the graphical Hopf bifurcation theorem, the system dynamics in a neighborhood of this singularity is explored. Also, with the aid of the package DDE-Biftool, some global bifurcations are detected in order to provide a better understanding of the whole scenario.
Fil: Gentile, Franco Sebastián. 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: Itovich, Griselda Rut. Universidad Nacional de Río Negro; 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
1:2 Resonance
Graphical Hopf Theorem
Time-Delay Systems
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:11336/64669
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedbackGentile, Franco SebastiánItovich, Griselda RutMoiola, Jorge Luis1:2 ResonanceGraphical Hopf TheoremTime-Delay Systemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work, the dynamics of an oscillator with delayed feedback is analyzed. It is found that for certain values of the parameters, the system exhibits a phenomenon known as double Hopf bifurcation with 1:2 resonance. This singularity provokes the interaction between two oscillatory solutions, one of frequency ω and the other with frequency 2 ω. By using the graphical Hopf bifurcation theorem, the system dynamics in a neighborhood of this singularity is explored. Also, with the aid of the package DDE-Biftool, some global bifurcations are detected in order to provide a better understanding of the whole scenario.Fil: Gentile, Franco Sebastián. 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: Itovich, Griselda Rut. Universidad Nacional de Río Negro; 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"; ArgentinaSpringer2018-02info: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/11336/64669Gentile, Franco Sebastián; Itovich, Griselda Rut; Moiola, Jorge Luis; Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback; Springer; Nonlinear Dynamics; 91; 3; 2-2018; 1779-17890924-090XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11071-017-3980-5info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11071-017-3980-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:44:01Zoai:ri.conicet.gov.ar:11336/64669instacron: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 09:44:01.445CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
title Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
spellingShingle Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
Gentile, Franco Sebastián
1:2 Resonance
Graphical Hopf Theorem
Time-Delay Systems
title_short Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
title_full Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
title_fullStr Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
title_full_unstemmed Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
title_sort Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback
dc.creator.none.fl_str_mv Gentile, Franco Sebastián
Itovich, Griselda Rut
Moiola, Jorge Luis
author Gentile, Franco Sebastián
author_facet Gentile, Franco Sebastián
Itovich, Griselda Rut
Moiola, Jorge Luis
author_role author
author2 Itovich, Griselda Rut
Moiola, Jorge Luis
author2_role author
author
dc.subject.none.fl_str_mv 1:2 Resonance
Graphical Hopf Theorem
Time-Delay Systems
topic 1:2 Resonance
Graphical Hopf Theorem
Time-Delay Systems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work, the dynamics of an oscillator with delayed feedback is analyzed. It is found that for certain values of the parameters, the system exhibits a phenomenon known as double Hopf bifurcation with 1:2 resonance. This singularity provokes the interaction between two oscillatory solutions, one of frequency ω and the other with frequency 2 ω. By using the graphical Hopf bifurcation theorem, the system dynamics in a neighborhood of this singularity is explored. Also, with the aid of the package DDE-Biftool, some global bifurcations are detected in order to provide a better understanding of the whole scenario.
Fil: Gentile, Franco Sebastián. 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: Itovich, Griselda Rut. Universidad Nacional de Río Negro; 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 an oscillator with delayed feedback is analyzed. It is found that for certain values of the parameters, the system exhibits a phenomenon known as double Hopf bifurcation with 1:2 resonance. This singularity provokes the interaction between two oscillatory solutions, one of frequency ω and the other with frequency 2 ω. By using the graphical Hopf bifurcation theorem, the system dynamics in a neighborhood of this singularity is explored. Also, with the aid of the package DDE-Biftool, some global bifurcations are detected in order to provide a better understanding of the whole scenario.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
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/11336/64669
Gentile, Franco Sebastián; Itovich, Griselda Rut; Moiola, Jorge Luis; Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback; Springer; Nonlinear Dynamics; 91; 3; 2-2018; 1779-1789
0924-090X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/64669
identifier_str_mv Gentile, Franco Sebastián; Itovich, Griselda Rut; Moiola, Jorge Luis; Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback; Springer; Nonlinear Dynamics; 91; 3; 2-2018; 1779-1789
0924-090X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11071-017-3980-5
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11071-017-3980-5
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 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
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score 13.070432

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