Generic bifurcations of planar filippov systems via geometric singular perturbations

Detalhes bibliográficos
Autor(a) principal: De Carvalho, Tiago [UNESP]
Data de Publicação: 2011
Outros Autores: Tonon, Durval José
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.36045/bbms/1323787173
http://hdl.handle.net/11449/219758
Resumo: In this paper we deal with non-smooth vector fields on the plane. We prove that the analysis of their local behavior around certain typical singularities can be treated via singular perturbation theory. In fact, after a regularization of a such system and a blow-up we are able to bring out some results that bridge the space between non-smooth dynamical systems presenting typical singularities and singularly perturbed smooth systems.
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spelling Generic bifurcations of planar filippov systems via geometric singular perturbationsBifurcationFold-fold singularityGeometric singular perturbationNon-smooth vector fieldsIn this paper we deal with non-smooth vector fields on the plane. We prove that the analysis of their local behavior around certain typical singularities can be treated via singular perturbation theory. In fact, after a regularization of a such system and a blow-up we are able to bring out some results that bridge the space between non-smooth dynamical systems presenting typical singularities and singularly perturbed smooth systems.IBILCE-UNESP, CEP 15054-000 S. J. Rio Preto, São PauloUniversidade Federal de Goiás IME, CEP 74001-970 Caixa Postal 131, Goiânia, GOIBILCE-UNESP, CEP 15054-000 S. J. Rio Preto, São PauloUniversidade Estadual Paulista (UNESP)Universidade Federal de Goiás (UFG)De Carvalho, Tiago [UNESP]Tonon, Durval José2022-04-28T18:57:20Z2022-04-28T18:57:20Z2011-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article861-881http://dx.doi.org/10.36045/bbms/1323787173Bulletin of the Belgian Mathematical Society - Simon Stevin, v. 18, n. 5 SUPPL., p. 861-881, 2011.1370-1444http://hdl.handle.net/11449/21975810.36045/bbms/13237871732-s2.0-84855645230Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBulletin of the Belgian Mathematical Society - Simon Stevininfo:eu-repo/semantics/openAccess2022-04-28T18:57:20Zoai:repositorio.unesp.br:11449/219758Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:30:38.387317Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Generic bifurcations of planar filippov systems via geometric singular perturbations
title Generic bifurcations of planar filippov systems via geometric singular perturbations
spellingShingle Generic bifurcations of planar filippov systems via geometric singular perturbations
De Carvalho, Tiago [UNESP]
Bifurcation
Fold-fold singularity
Geometric singular perturbation
Non-smooth vector fields
title_short Generic bifurcations of planar filippov systems via geometric singular perturbations
title_full Generic bifurcations of planar filippov systems via geometric singular perturbations
title_fullStr Generic bifurcations of planar filippov systems via geometric singular perturbations
title_full_unstemmed Generic bifurcations of planar filippov systems via geometric singular perturbations
title_sort Generic bifurcations of planar filippov systems via geometric singular perturbations
author De Carvalho, Tiago [UNESP]
author_facet De Carvalho, Tiago [UNESP]
Tonon, Durval José
author_role author
author2 Tonon, Durval José
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universidade Federal de Goiás (UFG)
dc.contributor.author.fl_str_mv De Carvalho, Tiago [UNESP]
Tonon, Durval José
dc.subject.por.fl_str_mv Bifurcation
Fold-fold singularity
Geometric singular perturbation
Non-smooth vector fields
topic Bifurcation
Fold-fold singularity
Geometric singular perturbation
Non-smooth vector fields
description In this paper we deal with non-smooth vector fields on the plane. We prove that the analysis of their local behavior around certain typical singularities can be treated via singular perturbation theory. In fact, after a regularization of a such system and a blow-up we are able to bring out some results that bridge the space between non-smooth dynamical systems presenting typical singularities and singularly perturbed smooth systems.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01
2022-04-28T18:57:20Z
2022-04-28T18:57:20Z
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/10.36045/bbms/1323787173
Bulletin of the Belgian Mathematical Society - Simon Stevin, v. 18, n. 5 SUPPL., p. 861-881, 2011.
1370-1444
http://hdl.handle.net/11449/219758
10.36045/bbms/1323787173
2-s2.0-84855645230
url http://dx.doi.org/10.36045/bbms/1323787173
http://hdl.handle.net/11449/219758
identifier_str_mv Bulletin of the Belgian Mathematical Society - Simon Stevin, v. 18, n. 5 SUPPL., p. 861-881, 2011.
1370-1444
10.36045/bbms/1323787173
2-s2.0-84855645230
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bulletin of the Belgian Mathematical Society - Simon Stevin
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 861-881
dc.source.none.fl_str_mv Scopus
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_ 1808128370993528832

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