Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field

We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive intege...

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Detalles Bibliográficos
Autores: Carvalho, Tiago [UNESP], Euźebio, Rodrigo D., Teixeira, Marco Antonto, Tonon, Durval Jośe
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/169891
Acceso en línea:http://dx.doi.org/10.1093/imamat/hxx003
http://hdl.handle.net/11449/169891
Access Level:acceso abierto
Palabra clave:Bifurcation
Limit cycles
Periodic solutions
Piecewise smooth vector fields
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spelling Birth of limit cycles from a 3D triangular center of a piecewise smooth vector fieldBifurcationLimit cyclesPeriodic solutionsPiecewise smooth vector fieldsWe consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive integer k, we produce suitable nonlinear small perturbations of the previous model and we obtain piecewise smooth vector fields having exactly k hyperbolic limit cycles instead of the center. Moreover, we also obtain suitable nonlinear small perturbations of the first model and piecewise smooth vector fields having a unique limit cycle of multiplicity k instead of the center. As consequence, the initial model has codimension infinity. Some aspects of asymptotical stability of such system are also addressed in this article.Universidade Federal de GoiásCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Departamento de Mateḿatica Faculdade de Ciências UNESP, Av. Eng. Luiz Edmundo Carrijo Coube 14-01Departamento de Mateḿatica Universidade Federal de Goías IME CEP 74001-970, Caixa Postal 131Departamento de Mateḿatica IMECC-UNICAMP CEP 13083-970Departamento de Mateḿatica Faculdade de Ciências UNESP, Av. Eng. Luiz Edmundo Carrijo Coube 14-01Universidade Federal de Goiás: 040393Universidade Federal de Goiás: 35796Universidade Federal de Goiás: 35798CAPES: 88881.030454/2013-01Universidade Estadual Paulista (Unesp)CEP 74001-970Universidade Estadual de Campinas (UNICAMP)2018-12-11T16:48:04Z2018-12-11T16:48:04Z2017-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article561-578application/pdfhttp://dx.doi.org/10.1093/imamat/hxx003IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 82, n. 3, p. 561-578, 2017.1464-36340272-4960http://hdl.handle.net/11449/16989110.1093/imamat/hxx0032-s2.0-850218141722-s2.0-85021814172.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)0,6790,679info:eu-repo/semantics/openAccessCarvalho, Tiago [UNESP]Euźebio, Rodrigo D.Teixeira, Marco AntontoTonon, Durval Jośe2025-06-24T05:48:05Zoai:repositorio.unesp.br:11449/169891Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-06-24T05:48:05Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
title Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
spellingShingle Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
Carvalho, Tiago [UNESP]
Bifurcation
Limit cycles
Periodic solutions
Piecewise smooth vector fields
title_short Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
title_full Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
title_fullStr Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
title_full_unstemmed Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
title_sort Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
dc.creator.none.fl_str_mv Carvalho, Tiago [UNESP]
Euźebio, Rodrigo D.
Teixeira, Marco Antonto
Tonon, Durval Jośe
author Carvalho, Tiago [UNESP]
author_facet Carvalho, Tiago [UNESP]
Euźebio, Rodrigo D.
Teixeira, Marco Antonto
Tonon, Durval Jośe
author_role author
author2 Euźebio, Rodrigo D.
Teixeira, Marco Antonto
Tonon, Durval Jośe
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
CEP 74001-970
Universidade Estadual de Campinas (UNICAMP)
dc.subject.por.fl_str_mv Bifurcation
Limit cycles
Periodic solutions
Piecewise smooth vector fields
topic Bifurcation
Limit cycles
Periodic solutions
Piecewise smooth vector fields
description We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive integer k, we produce suitable nonlinear small perturbations of the previous model and we obtain piecewise smooth vector fields having exactly k hyperbolic limit cycles instead of the center. Moreover, we also obtain suitable nonlinear small perturbations of the first model and piecewise smooth vector fields having a unique limit cycle of multiplicity k instead of the center. As consequence, the initial model has codimension infinity. Some aspects of asymptotical stability of such system are also addressed in this article.
publishDate 2017
dc.date.none.fl_str_mv 2017-01-01
2018-12-11T16:48:04Z
2018-12-11T16:48:04Z
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/hxx003
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 82, n. 3, p. 561-578, 2017.
1464-3634
0272-4960
http://hdl.handle.net/11449/169891
10.1093/imamat/hxx003
2-s2.0-85021814172
2-s2.0-85021814172.pdf
url http://dx.doi.org/10.1093/imamat/hxx003
http://hdl.handle.net/11449/169891
identifier_str_mv IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 82, n. 3, p. 561-578, 2017.
1464-3634
0272-4960
10.1093/imamat/hxx003
2-s2.0-85021814172
2-s2.0-85021814172.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
0,679
0,679
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 561-578
application/pdf
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 repositoriounesp@unesp.br
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score 15.301603

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