Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems

Detalhes bibliográficos
Autor(a) principal: de Carvalho Braga, Denis
Data de Publicação: 2020
Outros Autores: Fernandes da Fonseca, Alexander, Gonçalves, Luiz Fernando [UNESP], Mello, Luis Fernando
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.jmaa.2019.123692
http://hdl.handle.net/11449/198256
Resumo: We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov coefficients. As a consequence, the bifurcation diagrams, illustrating the number, types and positions of the bifurcating small amplitude crossing limit cycles for these vector fields, are determined.
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spelling Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systemsBifurcationFold-fold singularityHamiltonian vector fieldLimit cyclePiecewise smooth vector fieldWe study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov coefficients. As a consequence, the bifurcation diagrams, illustrating the number, types and positions of the bifurcating small amplitude crossing limit cycles for these vector fields, are determined.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Instituto de Matemática e Computação Universidade Federal de Itajubá, Avenida BPS 1303, Pinheirinho, CEP 37.500–903Instituto de Biociências Letras e Ciências Exatas UNESP, Rua Cristóvão Colombo, 2265, CEP 15054–000Instituto de Biociências Letras e Ciências Exatas UNESP, Rua Cristóvão Colombo, 2265, CEP 15054–000CAPES: 001FAPEMIG: APQ-01158-17Universidade Federal de ItajubáUniversidade Estadual Paulista (Unesp)de Carvalho Braga, DenisFernandes da Fonseca, AlexanderGonçalves, Luiz Fernando [UNESP]Mello, Luis Fernando2020-12-12T01:07:49Z2020-12-12T01:07:49Z2020-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jmaa.2019.123692Journal of Mathematical Analysis and Applications, v. 484, n. 1, 2020.1096-08130022-247Xhttp://hdl.handle.net/11449/19825610.1016/j.jmaa.2019.1236922-s2.0-85076222955Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Mathematical Analysis and Applicationsinfo:eu-repo/semantics/openAccess2021-10-23T10:11:10Zoai:repositorio.unesp.br:11449/198256Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T10:11:10Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
title Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
spellingShingle Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
de Carvalho Braga, Denis
Bifurcation
Fold-fold singularity
Hamiltonian vector field
Limit cycle
Piecewise smooth vector field
title_short Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
title_full Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
title_fullStr Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
title_full_unstemmed Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
title_sort Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
author de Carvalho Braga, Denis
author_facet de Carvalho Braga, Denis
Fernandes da Fonseca, Alexander
Gonçalves, Luiz Fernando [UNESP]
Mello, Luis Fernando
author_role author
author2 Fernandes da Fonseca, Alexander
Gonçalves, Luiz Fernando [UNESP]
Mello, Luis Fernando
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Federal de Itajubá
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv de Carvalho Braga, Denis
Fernandes da Fonseca, Alexander
Gonçalves, Luiz Fernando [UNESP]
Mello, Luis Fernando
dc.subject.por.fl_str_mv Bifurcation
Fold-fold singularity
Hamiltonian vector field
Limit cycle
Piecewise smooth vector field
topic Bifurcation
Fold-fold singularity
Hamiltonian vector field
Limit cycle
Piecewise smooth vector field
description We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov coefficients. As a consequence, the bifurcation diagrams, illustrating the number, types and positions of the bifurcating small amplitude crossing limit cycles for these vector fields, are determined.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T01:07:49Z
2020-12-12T01:07:49Z
2020-04-01
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/10.1016/j.jmaa.2019.123692
Journal of Mathematical Analysis and Applications, v. 484, n. 1, 2020.
1096-0813
0022-247X
http://hdl.handle.net/11449/198256
10.1016/j.jmaa.2019.123692
2-s2.0-85076222955
url http://dx.doi.org/10.1016/j.jmaa.2019.123692
http://hdl.handle.net/11449/198256
identifier_str_mv Journal of Mathematical Analysis and Applications, v. 484, n. 1, 2020.
1096-0813
0022-247X
10.1016/j.jmaa.2019.123692
2-s2.0-85076222955
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Mathematical Analysis and Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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_ 1799964659043794944

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