A proof of Perko's conjectures for the Bogdanov-Takens system

The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide...

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Autores: Gasull, Armengol|||0000-0002-1719-8231, Torregrosa, Joan|||0000-0002-2753-1827
Formato: artículo
Fecha de publicación:2013
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150601
Acesso em linha:https://ddd.uab.cat/record/150601
https://dx.doi.org/urn:doi:10.1016/j.jde.2013.07.006
Access Level:acceso abierto
Palavra-chave:Homoclinic connection
Location of limit cycles
Bifurcation of limit cycles
Global description of bifurcation curve
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spelling A proof of Perko's conjectures for the Bogdanov-Takens systemGasull, Armengol|||0000-0002-1719-8231Torregrosa, Joan|||0000-0002-2753-1827Homoclinic connectionLocation of limit cyclesBifurcation of limit cyclesGlobal description of bifurcation curveThe Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve. 22013-01-0120132013-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150601https://dx.doi.org/urn:doi:10.1016/j.jde.2013.07.006reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1506012026-06-06T12:50:31Z
dc.title.none.fl_str_mv A proof of Perko's conjectures for the Bogdanov-Takens system
title A proof of Perko's conjectures for the Bogdanov-Takens system
spellingShingle A proof of Perko's conjectures for the Bogdanov-Takens system
Gasull, Armengol|||0000-0002-1719-8231
Homoclinic connection
Location of limit cycles
Bifurcation of limit cycles
Global description of bifurcation curve
title_short A proof of Perko's conjectures for the Bogdanov-Takens system
title_full A proof of Perko's conjectures for the Bogdanov-Takens system
title_fullStr A proof of Perko's conjectures for the Bogdanov-Takens system
title_full_unstemmed A proof of Perko's conjectures for the Bogdanov-Takens system
title_sort A proof of Perko's conjectures for the Bogdanov-Takens system
dc.creator.none.fl_str_mv Gasull, Armengol|||0000-0002-1719-8231
Torregrosa, Joan|||0000-0002-2753-1827
author Gasull, Armengol|||0000-0002-1719-8231
author_facet Gasull, Armengol|||0000-0002-1719-8231
Torregrosa, Joan|||0000-0002-2753-1827
author_role author
author2 Torregrosa, Joan|||0000-0002-2753-1827
author2_role author
dc.subject.none.fl_str_mv Homoclinic connection
Location of limit cycles
Bifurcation of limit cycles
Global description of bifurcation curve
topic Homoclinic connection
Location of limit cycles
Bifurcation of limit cycles
Global description of bifurcation curve
description The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve.
publishDate 2013
dc.date.none.fl_str_mv 2
2013-01-01
2013
2013-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150601
https://dx.doi.org/urn:doi:10.1016/j.jde.2013.07.006
url https://ddd.uab.cat/record/150601
https://dx.doi.org/urn:doi:10.1016/j.jde.2013.07.006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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repository.mail.fl_str_mv
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