A Bendixson-Dulac theorem for some piecewise systems

The Bendixson-Dulac Theorem provides a criterion to find upper bounds for the number of limit cycles in analytic differential systems. We extend this classical result to some classes of piecewise differential systems. We apply it to three different Liénard piecewise differential systems ¨ x+f±(x)˙ x...

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Autores: Da Cruz, Leonardo Pereira Costa|||0000-0002-2853-4974, Torregrosa, Joan|||0000-0002-2753-1827
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:224216
Acceso en línea:https://ddd.uab.cat/record/224216
https://dx.doi.org/urn:doi:10.1088/1361-6544/ab6812
Access Level:acceso abierto
Palabra clave:Bendixson-Dulac theory
Piecewise vector field
Uniqueness of limit cycle
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spelling A Bendixson-Dulac theorem for some piecewise systemsDa Cruz, Leonardo Pereira Costa|||0000-0002-2853-4974Torregrosa, Joan|||0000-0002-2753-1827Bendixson-Dulac theoryPiecewise vector fieldUniqueness of limit cycleThe Bendixson-Dulac Theorem provides a criterion to find upper bounds for the number of limit cycles in analytic differential systems. We extend this classical result to some classes of piecewise differential systems. We apply it to three different Liénard piecewise differential systems ¨ x+f±(x)˙ x+x = 0. The first is linear, the second is rational and the last corresponds to a particular extension of the cubic van der Pol oscillator. In all cases, the systems present regions in the parameter space with no limit cycles and others having at most one. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/224216https://dx.doi.org/urn:doi:10.1088/1361-6544/ab6812reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617open 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:2242162026-06-06T12:50:31Z
dc.title.none.fl_str_mv A Bendixson-Dulac theorem for some piecewise systems
title A Bendixson-Dulac theorem for some piecewise systems
spellingShingle A Bendixson-Dulac theorem for some piecewise systems
Da Cruz, Leonardo Pereira Costa|||0000-0002-2853-4974
Bendixson-Dulac theory
Piecewise vector field
Uniqueness of limit cycle
title_short A Bendixson-Dulac theorem for some piecewise systems
title_full A Bendixson-Dulac theorem for some piecewise systems
title_fullStr A Bendixson-Dulac theorem for some piecewise systems
title_full_unstemmed A Bendixson-Dulac theorem for some piecewise systems
title_sort A Bendixson-Dulac theorem for some piecewise systems
dc.creator.none.fl_str_mv Da Cruz, Leonardo Pereira Costa|||0000-0002-2853-4974
Torregrosa, Joan|||0000-0002-2753-1827
author Da Cruz, Leonardo Pereira Costa|||0000-0002-2853-4974
author_facet Da Cruz, Leonardo Pereira Costa|||0000-0002-2853-4974
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 Bendixson-Dulac theory
Piecewise vector field
Uniqueness of limit cycle
topic Bendixson-Dulac theory
Piecewise vector field
Uniqueness of limit cycle
description The Bendixson-Dulac Theorem provides a criterion to find upper bounds for the number of limit cycles in analytic differential systems. We extend this classical result to some classes of piecewise differential systems. We apply it to three different Liénard piecewise differential systems ¨ x+f±(x)˙ x+x = 0. The first is linear, the second is rational and the last corresponds to a particular extension of the cubic van der Pol oscillator. In all cases, the systems present regions in the parameter space with no limit cycles and others having at most one.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
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/224216
https://dx.doi.org/urn:doi:10.1088/1361-6544/ab6812
url https://ddd.uab.cat/record/224216
https://dx.doi.org/urn:doi:10.1088/1361-6544/ab6812
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
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
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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