Limit cycles of a class of generalized Liénard polynomial equations

We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.

Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Makhlouf, Ammar
Formato: artículo
Fecha de publicación:2015
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:145358
Acesso em linha:https://ddd.uab.cat/record/145358
https://dx.doi.org/urn:doi:10.1007/s10883-014-9253-4
Access Level:acceso abierto
Palavra-chave:Averaging theory
Liénard system
Limit cycles
Polynomial differential systems
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spelling Limit cycles of a class of generalized Liénard polynomial equationsLlibre, Jaume|||0000-0002-9511-5999Makhlouf, AmmarAveraging theoryLiénard systemLimit cyclesPolynomial differential systemsWe prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x. 22015-01-0120152015-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/145358https://dx.doi.org/urn:doi:10.1007/s10883-014-9253-4reponame: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 2014/SGR-410European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 318999open 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:1453582026-06-06T12:50:31Z
dc.title.none.fl_str_mv Limit cycles of a class of generalized Liénard polynomial equations
title Limit cycles of a class of generalized Liénard polynomial equations
spellingShingle Limit cycles of a class of generalized Liénard polynomial equations
Llibre, Jaume|||0000-0002-9511-5999
Averaging theory
Liénard system
Limit cycles
Polynomial differential systems
title_short Limit cycles of a class of generalized Liénard polynomial equations
title_full Limit cycles of a class of generalized Liénard polynomial equations
title_fullStr Limit cycles of a class of generalized Liénard polynomial equations
title_full_unstemmed Limit cycles of a class of generalized Liénard polynomial equations
title_sort Limit cycles of a class of generalized Liénard polynomial equations
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Makhlouf, Ammar
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Makhlouf, Ammar
author_role author
author2 Makhlouf, Ammar
author2_role author
dc.subject.none.fl_str_mv Averaging theory
Liénard system
Limit cycles
Polynomial differential systems
topic Averaging theory
Liénard system
Limit cycles
Polynomial differential systems
description We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.
publishDate 2015
dc.date.none.fl_str_mv 2
2015-01-01
2015
2015-01-01
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/145358
https://dx.doi.org/urn:doi:10.1007/s10883-014-9253-4
url https://ddd.uab.cat/record/145358
https://dx.doi.org/urn:doi:10.1007/s10883-014-9253-4
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 2014/SGR-410
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 318999
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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