Piecewise linear differential systems with two real saddles

In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to a...

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Autores: Artés Ferragud, Joan Carles|||0000-0003-4332-7495, Llibre, Jaume|||0000-0002-9511-5999, Medrado, Joao Carlos|||0000-0001-5042-9110, Teixeira, Marco Antonio|||0000-0002-5386-9282
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150653
Acceso en línea:https://ddd.uab.cat/record/150653
https://dx.doi.org/urn:doi:10.1016/j.matcom.2013.02.007
Access Level:acceso abierto
Palabra clave:Non-smooth differential system
Limit cycle
Piecewise linear differential system
Hopf bifurcation
Sliding limit cycle
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spelling Piecewise linear differential systems with two real saddlesArtés Ferragud, Joan Carles|||0000-0003-4332-7495Llibre, Jaume|||0000-0002-9511-5999Medrado, Joao Carlos|||0000-0001-5042-9110Teixeira, Marco Antonio|||0000-0002-5386-9282Non-smooth differential systemLimit cyclePiecewise linear differential systemHopf bifurcationSliding limit cycleIn this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a generalized singular point on the line. This point is a focus or a center and there can be found limit cycles around it. We are going to show that the maximum number of limit cycles that can bifurcate from this focus is two. One of them appears through a Hopf bifurcation and the second when the focus becomes a node by means of the sliding. 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/150653https://dx.doi.org/urn:doi:10.1016/j.matcom.2013.02.007reponame: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:1506532026-06-06T12:50:31Z
dc.title.none.fl_str_mv Piecewise linear differential systems with two real saddles
title Piecewise linear differential systems with two real saddles
spellingShingle Piecewise linear differential systems with two real saddles
Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Non-smooth differential system
Limit cycle
Piecewise linear differential system
Hopf bifurcation
Sliding limit cycle
title_short Piecewise linear differential systems with two real saddles
title_full Piecewise linear differential systems with two real saddles
title_fullStr Piecewise linear differential systems with two real saddles
title_full_unstemmed Piecewise linear differential systems with two real saddles
title_sort Piecewise linear differential systems with two real saddles
dc.creator.none.fl_str_mv Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Llibre, Jaume|||0000-0002-9511-5999
Medrado, Joao Carlos|||0000-0001-5042-9110
Teixeira, Marco Antonio|||0000-0002-5386-9282
author Artés Ferragud, Joan Carles|||0000-0003-4332-7495
author_facet Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Llibre, Jaume|||0000-0002-9511-5999
Medrado, Joao Carlos|||0000-0001-5042-9110
Teixeira, Marco Antonio|||0000-0002-5386-9282
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Medrado, Joao Carlos|||0000-0001-5042-9110
Teixeira, Marco Antonio|||0000-0002-5386-9282
author2_role author
author
author
dc.subject.none.fl_str_mv Non-smooth differential system
Limit cycle
Piecewise linear differential system
Hopf bifurcation
Sliding limit cycle
topic Non-smooth differential system
Limit cycle
Piecewise linear differential system
Hopf bifurcation
Sliding limit cycle
description In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a generalized singular point on the line. This point is a focus or a center and there can be found limit cycles around it. We are going to show that the maximum number of limit cycles that can bifurcate from this focus is two. One of them appears through a Hopf bifurcation and the second when the focus becomes a node by means of the sliding.
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
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dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150653
https://dx.doi.org/urn:doi:10.1016/j.matcom.2013.02.007
url https://ddd.uab.cat/record/150653
https://dx.doi.org/urn:doi:10.1016/j.matcom.2013.02.007
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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