On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities

Detalhes bibliográficos
Autor(a) principal: Novaes, Douglas D.
Data de Publicação: 2022
Outros Autores: Rondón, Gabriel [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.physd.2022.133526
http://hdl.handle.net/11449/245992
Resumo: In this paper, we are concerned about smoothing of Filippov systems around homoclinic-like connections to regular-tangential singularities. We provide conditions to guarantee the existence of limit cycles bifurcating from such connections. Additional conditions are also provided to ensure the stability and uniqueness of such limit cycles. All the proofs are based on the construction of the first return map of the regularized Filippov system around homoclinic-like connections. Such a map is obtained by using a recent characterization of the local behavior of the regularized Filippov system around regular-tangential singularities. Fixed point theorems and Poincaré–Bendixson arguments are also employed.
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spelling On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularitiesLimit cyclesNonsmooth differential systemsRegularizationTangential singularitiesΣ–polycyclesIn this paper, we are concerned about smoothing of Filippov systems around homoclinic-like connections to regular-tangential singularities. We provide conditions to guarantee the existence of limit cycles bifurcating from such connections. Additional conditions are also provided to ensure the stability and uniqueness of such limit cycles. All the proofs are based on the construction of the first return map of the regularized Filippov system around homoclinic-like connections. Such a map is obtained by using a recent characterization of the local behavior of the regularized Filippov system around regular-tangential singularities. Fixed point theorems and Poincaré–Bendixson arguments are also employed.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Departamento de Matemática Instituto de Matemática Estatística e Computação Científica (IMECC) Universidade Estadual de Campinas (UNICAMP), Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz, SPUNESP - Universidade Estadual Paulista São José do Rio PretoUNESP - Universidade Estadual Paulista São José do Rio PretoFAPESP: 2018/13481-0FAPESP: 2019/10269-3FAPESP: 2020/06708-9FAPESP: 2021/10606-0CNPq: 309110/2021-1CNPq: 438975/2018-9Universidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (UNESP)Novaes, Douglas D.Rondón, Gabriel [UNESP]2023-07-29T12:28:49Z2023-07-29T12:28:49Z2022-12-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.physd.2022.133526Physica D: Nonlinear Phenomena, v. 442.0167-2789http://hdl.handle.net/11449/24599210.1016/j.physd.2022.1335262-s2.0-85139065582Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysica D: Nonlinear Phenomenainfo:eu-repo/semantics/openAccess2023-07-29T12:28:49Zoai:repositorio.unesp.br:11449/245992Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:59:32.462105Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
title On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
spellingShingle On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
Novaes, Douglas D.
Limit cycles
Nonsmooth differential systems
Regularization
Tangential singularities
Σ–polycycles
title_short On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
title_full On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
title_fullStr On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
title_full_unstemmed On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
title_sort On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
author Novaes, Douglas D.
author_facet Novaes, Douglas D.
Rondón, Gabriel [UNESP]
author_role author
author2 Rondón, Gabriel [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Novaes, Douglas D.
Rondón, Gabriel [UNESP]
dc.subject.por.fl_str_mv Limit cycles
Nonsmooth differential systems
Regularization
Tangential singularities
Σ–polycycles
topic Limit cycles
Nonsmooth differential systems
Regularization
Tangential singularities
Σ–polycycles
description In this paper, we are concerned about smoothing of Filippov systems around homoclinic-like connections to regular-tangential singularities. We provide conditions to guarantee the existence of limit cycles bifurcating from such connections. Additional conditions are also provided to ensure the stability and uniqueness of such limit cycles. All the proofs are based on the construction of the first return map of the regularized Filippov system around homoclinic-like connections. Such a map is obtained by using a recent characterization of the local behavior of the regularized Filippov system around regular-tangential singularities. Fixed point theorems and Poincaré–Bendixson arguments are also employed.
publishDate 2022
dc.date.none.fl_str_mv 2022-12-15
2023-07-29T12:28:49Z
2023-07-29T12:28:49Z
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.physd.2022.133526
Physica D: Nonlinear Phenomena, v. 442.
0167-2789
http://hdl.handle.net/11449/245992
10.1016/j.physd.2022.133526
2-s2.0-85139065582
url http://dx.doi.org/10.1016/j.physd.2022.133526
http://hdl.handle.net/11449/245992
identifier_str_mv Physica D: Nonlinear Phenomena, v. 442.
0167-2789
10.1016/j.physd.2022.133526
2-s2.0-85139065582
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physica D: Nonlinear Phenomena
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
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