Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles tha...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Zhang, Xiang|||0000-0001-5194-4077
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:199322
Acceso en línea:https://ddd.uab.cat/record/199322
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024
Access Level:acceso abierto
Palabra clave:Discontinuous piecewise linear differential system
Limit cycle
Non-smooth differential system
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spelling Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a centerLlibre, Jaume|||0000-0002-9511-5999Zhang, Xiang|||0000-0001-5194-4077Discontinuous piecewise linear differential systemLimit cycleNon-smooth differential systemFrom the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. 22018-01-0120182018-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/199322https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568open 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:1993222026-06-06T12:50:31Z
dc.title.none.fl_str_mv Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
title Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
spellingShingle Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
Llibre, Jaume|||0000-0002-9511-5999
Discontinuous piecewise linear differential system
Limit cycle
Non-smooth differential system
title_short Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
title_full Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
title_fullStr Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
title_full_unstemmed Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
title_sort Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Zhang, Xiang|||0000-0001-5194-4077
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Zhang, Xiang|||0000-0001-5194-4077
author_role author
author2 Zhang, Xiang|||0000-0001-5194-4077
author2_role author
dc.subject.none.fl_str_mv Discontinuous piecewise linear differential system
Limit cycle
Non-smooth differential system
topic Discontinuous piecewise linear differential system
Limit cycle
Non-smooth differential system
description From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles.
publishDate 2018
dc.date.none.fl_str_mv 2
2018-01-01
2018
2018-01-01
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/199322
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024
url https://ddd.uab.cat/record/199322
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
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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