Limit cycles bifurcating from discontinuous centres

Detalhes bibliográficos
Autor(a) principal: Braga, Denis de Carvalho
Data de Publicação: 2017
Outros Autores: Carvalho, Tiago [UNESP], Mello, Luis Fernando
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1093/imamat/hxx017
http://hdl.handle.net/11449/163118
Resumo: In this article, we study limit cycles in discontinuous piecewise linear vector fields in R-2 and R-3. More precisely, we address the problem of understanding the dynamics around a degenerated two-fold singularity in R-2 and R-3, where it is also called T-singularity, which behave as discontinuous centres after suitable perturbations of the separation boundaries. We prove that, in both systems, it is possible to obtain k hyperbolic limit cycles bifurcating from these discontinuous centres, for any positive integer k. The same holds if k is infinity.
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spelling Limit cycles bifurcating from discontinuous centresbifurcationlimit cyclenon-smooth vector fieldT-singularitytwo-fold singularityIn this article, we study limit cycles in discontinuous piecewise linear vector fields in R-2 and R-3. More precisely, we address the problem of understanding the dynamics around a degenerated two-fold singularity in R-2 and R-3, where it is also called T-singularity, which behave as discontinuous centres after suitable perturbations of the separation boundaries. We prove that, in both systems, it is possible to obtain k hyperbolic limit cycles bifurcating from these discontinuous centres, for any positive integer k. The same holds if k is infinity.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Univ Fed Itajuba, Inst Matemat & Computacao, Ave BPS 1303, BR-37500903 Itajuba, MG, BrazilUniv Estadual Paulista, Dept Matemat, Rua Engn Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, BrazilUniv Estadual Paulista, Dept Matemat, Rua Engn Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, BrazilFAPESP: 2014/02134-7CNPq: 443302/2014-6CAPES: 1576689CAPES: 88881.030454/2013-01FAPEMIG: PPM-00516-15CAPES: 88881.119020/2016-01Oxford Univ PressUniv Fed ItajubaUniversidade Estadual Paulista (Unesp)Braga, Denis de CarvalhoCarvalho, Tiago [UNESP]Mello, Luis Fernando2018-11-26T17:40:11Z2018-11-26T17:40:11Z2017-08-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article849-863application/pdfhttp://dx.doi.org/10.1093/imamat/hxx017Ima Journal Of Applied Mathematics. Oxford: Oxford Univ Press, v. 82, n. 4, p. 849-863, 2017.0272-4960http://hdl.handle.net/11449/16311810.1093/imamat/hxx017WOS:000407267000009WOS000407267000009.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIma Journal Of Applied Mathematics0,679info:eu-repo/semantics/openAccess2024-04-29T14:59:43Zoai:repositorio.unesp.br:11449/163118Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-04-29T14:59:43Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Limit cycles bifurcating from discontinuous centres
title Limit cycles bifurcating from discontinuous centres
spellingShingle Limit cycles bifurcating from discontinuous centres
Braga, Denis de Carvalho
bifurcation
limit cycle
non-smooth vector field
T-singularity
two-fold singularity
title_short Limit cycles bifurcating from discontinuous centres
title_full Limit cycles bifurcating from discontinuous centres
title_fullStr Limit cycles bifurcating from discontinuous centres
title_full_unstemmed Limit cycles bifurcating from discontinuous centres
title_sort Limit cycles bifurcating from discontinuous centres
author Braga, Denis de Carvalho
author_facet Braga, Denis de Carvalho
Carvalho, Tiago [UNESP]
Mello, Luis Fernando
author_role author
author2 Carvalho, Tiago [UNESP]
Mello, Luis Fernando
author2_role author
author
dc.contributor.none.fl_str_mv Univ Fed Itajuba
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Braga, Denis de Carvalho
Carvalho, Tiago [UNESP]
Mello, Luis Fernando
dc.subject.por.fl_str_mv bifurcation
limit cycle
non-smooth vector field
T-singularity
two-fold singularity
topic bifurcation
limit cycle
non-smooth vector field
T-singularity
two-fold singularity
description In this article, we study limit cycles in discontinuous piecewise linear vector fields in R-2 and R-3. More precisely, we address the problem of understanding the dynamics around a degenerated two-fold singularity in R-2 and R-3, where it is also called T-singularity, which behave as discontinuous centres after suitable perturbations of the separation boundaries. We prove that, in both systems, it is possible to obtain k hyperbolic limit cycles bifurcating from these discontinuous centres, for any positive integer k. The same holds if k is infinity.
publishDate 2017
dc.date.none.fl_str_mv 2017-08-01
2018-11-26T17:40:11Z
2018-11-26T17:40:11Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1093/imamat/hxx017
Ima Journal Of Applied Mathematics. Oxford: Oxford Univ Press, v. 82, n. 4, p. 849-863, 2017.
0272-4960
http://hdl.handle.net/11449/163118
10.1093/imamat/hxx017
WOS:000407267000009
WOS000407267000009.pdf
url http://dx.doi.org/10.1093/imamat/hxx017
http://hdl.handle.net/11449/163118
identifier_str_mv Ima Journal Of Applied Mathematics. Oxford: Oxford Univ Press, v. 82, n. 4, p. 849-863, 2017.
0272-4960
10.1093/imamat/hxx017
WOS:000407267000009
WOS000407267000009.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Ima Journal Of Applied Mathematics
0,679
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 849-863
application/pdf
dc.publisher.none.fl_str_mv Oxford Univ Press
publisher.none.fl_str_mv Oxford Univ Press
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1803047142619611136

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