On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities

We consider the class of polynomial differential equations ˙x = λx + Pn(x, y), y˙ = µy + Qn(x, y) in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= µ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneo...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Yu, Jiang, Zhang, Xiang|||0000-0001-5194-4077
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150722
Acceso en línea:https://ddd.uab.cat/record/150722
https://dx.doi.org/urn:doi:10.1142/S0218127414500655
Access Level:acceso abierto
Palabra clave:Homogeneous nonlinearities
Limit cycles
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spelling On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearitiesLlibre, Jaume|||0000-0002-9511-5999Yu, JiangZhang, Xiang|||0000-0001-5194-4077Homogeneous nonlinearitiesLimit cyclesWe consider the class of polynomial differential equations ˙x = λx + Pn(x, y), y˙ = µy + Qn(x, y) in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= µ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations we study the existence and non-existence of limit cycles surrounding the node localized at the origin of coordinates. 22014-01-0120142014-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150722https://dx.doi.org/urn:doi:10.1142/S0218127414500655reponame: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 2009/SGR-410European 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:1507222026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
title On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
spellingShingle On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
Llibre, Jaume|||0000-0002-9511-5999
Homogeneous nonlinearities
Limit cycles
title_short On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
title_full On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
title_fullStr On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
title_full_unstemmed On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
title_sort On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Yu, Jiang
Zhang, Xiang|||0000-0001-5194-4077
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Yu, Jiang
Zhang, Xiang|||0000-0001-5194-4077
author_role author
author2 Yu, Jiang
Zhang, Xiang|||0000-0001-5194-4077
author2_role author
author
dc.subject.none.fl_str_mv Homogeneous nonlinearities
Limit cycles
topic Homogeneous nonlinearities
Limit cycles
description We consider the class of polynomial differential equations ˙x = λx + Pn(x, y), y˙ = µy + Qn(x, y) in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= µ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations we study the existence and non-existence of limit cycles surrounding the node localized at the origin of coordinates.
publishDate 2014
dc.date.none.fl_str_mv 2
2014-01-01
2014
2014-01-01
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/150722
https://dx.doi.org/urn:doi:10.1142/S0218127414500655
url https://ddd.uab.cat/record/150722
https://dx.doi.org/urn:doi:10.1142/S0218127414500655
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 2009/SGR-410
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
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eu_rights_str_mv openAccess
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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
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