Limit cycles bifurcating from discontinuous centres
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
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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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 |