Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems

The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differentia...

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Detalles Bibliográficos
Autores: Li, Jie|||0000-0003-0134-7674, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:287940
Acceso en línea:https://ddd.uab.cat/record/287940
https://dx.doi.org/urn:doi:10.1007/s12591-023-00666-7
Access Level:acceso abierto
Palabra clave:Continuous piecewise linear differential system
Phase portrait
Limit cycle
Poincaré disc
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spelling Phase Portraits of a Class of Continuous Piecewise Linear Differential SystemsLi, Jie|||0000-0003-0134-7674Llibre, Jaume|||0000-0002-9511-5999Continuous piecewise linear differential systemPhase portraitLimit cyclePoincaré discThe phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. Note that on the straight line x= 0 these differential systems are only continuous. 22025-01-0120252025-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/287940https://dx.doi.org/urn:doi:10.1007/s12591-023-00666-7reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengEuropean Commission https://doi.org/10.13039/501100000780 777911Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2022/SGR-00113Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2879402026-06-06T12:50:31Z
dc.title.none.fl_str_mv Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
title Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
spellingShingle Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
Li, Jie|||0000-0003-0134-7674
Continuous piecewise linear differential system
Phase portrait
Limit cycle
Poincaré disc
title_short Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
title_full Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
title_fullStr Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
title_full_unstemmed Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
title_sort Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems
dc.creator.none.fl_str_mv Li, Jie|||0000-0003-0134-7674
Llibre, Jaume|||0000-0002-9511-5999
author Li, Jie|||0000-0003-0134-7674
author_facet Li, Jie|||0000-0003-0134-7674
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Continuous piecewise linear differential system
Phase portrait
Limit cycle
Poincaré disc
topic Continuous piecewise linear differential system
Phase portrait
Limit cycle
Poincaré disc
description The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. Note that on the straight line x= 0 these differential systems are only continuous.
publishDate 2025
dc.date.none.fl_str_mv 2
2025-01-01
2025
2025-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/287940
https://dx.doi.org/urn:doi:10.1007/s12591-023-00666-7
url https://ddd.uab.cat/record/287940
https://dx.doi.org/urn:doi:10.1007/s12591-023-00666-7
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission https://doi.org/10.13039/501100000780 777911
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2022/SGR-00113
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
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://creativecommons.org/licenses/by/4.0/
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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