Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory

In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the pe...

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Autores: Benterki, Rebiha|||0000-0001-6745-2747, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169499
Acceso en línea:https://ddd.uab.cat/record/169499
https://dx.doi.org/urn:doi:10.1016/j.cam.2016.08.047
Access Level:acceso abierto
Palabra clave:Averaging method
Center
Generalized Kukles system
Limit cycle
Phase portrait
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spelling Centers and limit cycles of polynomial differential systems of degree 4 via averaging theoryBenterki, Rebiha|||0000-0001-6745-2747Llibre, Jaume|||0000-0002-9511-5999Averaging methodCenterGeneralized Kukles systemLimit cyclePhase portraitIn this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4. 22017-01-0120172017-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/169499https://dx.doi.org/urn:doi:10.1016/j.cam.2016.08.047reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio 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-568European Commission https://doi.org/10.13039/501100000780 318999European Commission https://doi.org/10.13039/501100000780 316338open 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:1694992026-06-06T12:50:31Z
dc.title.none.fl_str_mv Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
title Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
spellingShingle Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
Benterki, Rebiha|||0000-0001-6745-2747
Averaging method
Center
Generalized Kukles system
Limit cycle
Phase portrait
title_short Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
title_full Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
title_fullStr Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
title_full_unstemmed Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
title_sort Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory
dc.creator.none.fl_str_mv Benterki, Rebiha|||0000-0001-6745-2747
Llibre, Jaume|||0000-0002-9511-5999
author Benterki, Rebiha|||0000-0001-6745-2747
author_facet Benterki, Rebiha|||0000-0001-6745-2747
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 Averaging method
Center
Generalized Kukles system
Limit cycle
Phase portrait
topic Averaging method
Center
Generalized Kukles system
Limit cycle
Phase portrait
description In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.
publishDate 2017
dc.date.none.fl_str_mv 2
2017-01-01
2017
2017-01-01
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/169499
https://dx.doi.org/urn:doi:10.1016/j.cam.2016.08.047
url https://ddd.uab.cat/record/169499
https://dx.doi.org/urn:doi:10.1016/j.cam.2016.08.047
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 MTM2013-40998-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
European Commission https://doi.org/10.13039/501100000780 318999
European Commission https://doi.org/10.13039/501100000780 316338
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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