Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields

Detalhes bibliográficos
Autor(a) principal: Santana, Paulo [UNESP]
Data de Publicação: 2023
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s12346-023-00838-4
https://hdl.handle.net/11449/297873
Resumo: In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may contain hyperbolic saddles, semi-hyperbolic saddles, saddle-nodes and tangential singularities of any degree. We determine when the polycycle is stable or unstable. We prove the bifurcation of at most one limit cycle in some conditions and at least one limit cycle for each singularity in other conditions.
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spelling Stability and Cyclicity of Polycycles in Non-smooth Planar Vector FieldsAgeingFilippovHidden dynamicsMixed-modeNonsmoothPiecewiseSwitchingIn this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may contain hyperbolic saddles, semi-hyperbolic saddles, saddle-nodes and tangential singularities of any degree. We determine when the polycycle is stable or unstable. We prove the bifurcation of at most one limit cycle in some conditions and at least one limit cycle for each singularity in other conditions.IBILCE–UNESP, São PauloIBILCE–UNESP, São PauloUniversidade Estadual Paulista (UNESP)Santana, Paulo [UNESP]2025-04-29T18:35:29Z2023-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s12346-023-00838-4Qualitative Theory of Dynamical Systems, v. 22, n. 4, 2023.1662-35921575-5460https://hdl.handle.net/11449/29787310.1007/s12346-023-00838-42-s2.0-85166241087Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengQualitative Theory of Dynamical Systemsinfo:eu-repo/semantics/openAccess2025-04-30T13:53:12Zoai:repositorio.unesp.br:11449/297873Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T13:53:12Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
title Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
spellingShingle Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
Santana, Paulo [UNESP]
Ageing
Filippov
Hidden dynamics
Mixed-mode
Nonsmooth
Piecewise
Switching
title_short Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
title_full Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
title_fullStr Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
title_full_unstemmed Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
title_sort Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields
author Santana, Paulo [UNESP]
author_facet Santana, Paulo [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Santana, Paulo [UNESP]
dc.subject.por.fl_str_mv Ageing
Filippov
Hidden dynamics
Mixed-mode
Nonsmooth
Piecewise
Switching
topic Ageing
Filippov
Hidden dynamics
Mixed-mode
Nonsmooth
Piecewise
Switching
description In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may contain hyperbolic saddles, semi-hyperbolic saddles, saddle-nodes and tangential singularities of any degree. We determine when the polycycle is stable or unstable. We prove the bifurcation of at most one limit cycle in some conditions and at least one limit cycle for each singularity in other conditions.
publishDate 2023
dc.date.none.fl_str_mv 2023-12-01
2025-04-29T18:35:29Z
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/10.1007/s12346-023-00838-4
Qualitative Theory of Dynamical Systems, v. 22, n. 4, 2023.
1662-3592
1575-5460
https://hdl.handle.net/11449/297873
10.1007/s12346-023-00838-4
2-s2.0-85166241087
url http://dx.doi.org/10.1007/s12346-023-00838-4
https://hdl.handle.net/11449/297873
identifier_str_mv Qualitative Theory of Dynamical Systems, v. 22, n. 4, 2023.
1662-3592
1575-5460
10.1007/s12346-023-00838-4
2-s2.0-85166241087
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Qualitative Theory of Dynamical Systems
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 repositoriounesp@unesp.br
_version_ 1834482907189608448

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