On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center

While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the lim...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Salhi, Tayeb|||0000-0003-1220-592X
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:267136
Acceso en línea:https://ddd.uab.cat/record/267136
https://dx.doi.org/urn:doi:10.1016/j.chaos.2022.112256
Access Level:acceso abierto
Palabra clave:Linear focus
Linear center
Quadratic weak focus
Quadratic center
Limit cycle
Discontinuous piecewise differential system
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spelling On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or centerLlibre, Jaume|||0000-0002-9511-5999Salhi, Tayeb|||0000-0003-1220-592XLinear focusLinear centerQuadratic weak focusQuadratic centerLimit cycleDiscontinuous piecewise differential systemWhile the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/267136https://dx.doi.org/urn:doi:10.1016/j.chaos.2022.112256reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00European Commission https://doi.org/10.13039/501100000780 777911open 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, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2671362026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
title On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
spellingShingle On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
Llibre, Jaume|||0000-0002-9511-5999
Linear focus
Linear center
Quadratic weak focus
Quadratic center
Limit cycle
Discontinuous piecewise differential system
title_short On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
title_full On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
title_fullStr On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
title_full_unstemmed On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
title_sort On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Salhi, Tayeb|||0000-0003-1220-592X
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Salhi, Tayeb|||0000-0003-1220-592X
author_role author
author2 Salhi, Tayeb|||0000-0003-1220-592X
author2_role author
dc.subject.none.fl_str_mv Linear focus
Linear center
Quadratic weak focus
Quadratic center
Limit cycle
Discontinuous piecewise differential system
topic Linear focus
Linear center
Quadratic weak focus
Quadratic center
Limit cycle
Discontinuous piecewise differential system
description While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
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/267136
https://dx.doi.org/urn:doi:10.1016/j.chaos.2022.112256
url https://ddd.uab.cat/record/267136
https://dx.doi.org/urn:doi:10.1016/j.chaos.2022.112256
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/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-nc-nd/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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