Local cyclicity in low degree planar piecewise polynomial vector fields

Detalhes bibliográficos
Autor(a) principal: Gouveia, Luiz F. S. [UNESP]
Data de Publicação: 2021
Outros Autores: Torregrosa, Joan
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.nonrwa.2020.103278
http://hdl.handle.net/11449/210159
Resumo: In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding segment. We provide lower bounds for the local cyclicity for planar piecewise polynomial systems, M-c(p)(n), with degrees 2, 3, 4, and 5. More concretely, Mc p (2) >= 13, M-c(p) (3) >= 26, M-c(p) (4) >= 40, and M-c(p) (5) >= 58. The computations use parallelization algorithms. (C) 2020 Elsevier Ltd. All rights reserved.
id UNSP_e20396951673a1b4ba079f29f709cfa3
oai_identifier_str oai:repositorio.unesp.br:11449/210159
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling Local cyclicity in low degree planar piecewise polynomial vector fieldsPiecewise vector fieldPiecewise center cyclicityLyapunov quantitiesIn this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding segment. We provide lower bounds for the local cyclicity for planar piecewise polynomial systems, M-c(p)(n), with degrees 2, 3, 4, and 5. More concretely, Mc p (2) >= 13, M-c(p) (3) >= 26, M-c(p) (4) >= 40, and M-c(p) (5) >= 58. The computations use parallelization algorithms. (C) 2020 Elsevier Ltd. All rights reserved.AGAURMinisterio de Ciencia, Innovacion y Universidades, Spain -Agencia Estatal de InvestigacionEuropean CommunityConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, SpainUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, BrazilCtr Recerca Matemat, Campus Bellaterra, Barcelona 08193, SpainUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, BrazilAGAUR: 2017 SGR 1617Ministerio de Ciencia, Innovacion y Universidades, Spain -Agencia Estatal de Investigacion: MTM2016-77278-PMinisterio de Ciencia, Innovacion y Universidades, Spain -Agencia Estatal de Investigacion: PID2019-104658GB-I00European Community: H2020-MSCA-RISE-2017-777911CNPq: 200484/2015-0FAPESP: 2020/04717-0Elsevier B.V.Univ Autonoma BarcelonaUniversidade Estadual Paulista (Unesp)Ctr Recerca MatematGouveia, Luiz F. S. [UNESP]Torregrosa, Joan2021-06-25T12:41:24Z2021-06-25T12:41:24Z2021-08-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article19http://dx.doi.org/10.1016/j.nonrwa.2020.103278Nonlinear Analysis-real World Applications. Oxford: Pergamon-elsevier Science Ltd, v. 60, 19 p., 2021.1468-1218http://hdl.handle.net/11449/21015910.1016/j.nonrwa.2020.103278WOS:000633361700001Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Analysis-real World Applicationsinfo:eu-repo/semantics/openAccess2021-10-23T20:11:16Zoai:repositorio.unesp.br:11449/210159Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:07:46.323521Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Local cyclicity in low degree planar piecewise polynomial vector fields
title Local cyclicity in low degree planar piecewise polynomial vector fields
spellingShingle Local cyclicity in low degree planar piecewise polynomial vector fields
Gouveia, Luiz F. S. [UNESP]
Piecewise vector field
Piecewise center cyclicity
Lyapunov quantities
title_short Local cyclicity in low degree planar piecewise polynomial vector fields
title_full Local cyclicity in low degree planar piecewise polynomial vector fields
title_fullStr Local cyclicity in low degree planar piecewise polynomial vector fields
title_full_unstemmed Local cyclicity in low degree planar piecewise polynomial vector fields
title_sort Local cyclicity in low degree planar piecewise polynomial vector fields
author Gouveia, Luiz F. S. [UNESP]
author_facet Gouveia, Luiz F. S. [UNESP]
Torregrosa, Joan
author_role author
author2 Torregrosa, Joan
author2_role author
dc.contributor.none.fl_str_mv Univ Autonoma Barcelona
Universidade Estadual Paulista (Unesp)
Ctr Recerca Matemat
dc.contributor.author.fl_str_mv Gouveia, Luiz F. S. [UNESP]
Torregrosa, Joan
dc.subject.por.fl_str_mv Piecewise vector field
Piecewise center cyclicity
Lyapunov quantities
topic Piecewise vector field
Piecewise center cyclicity
Lyapunov quantities
description In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. They are all nested and surrounding one equilibrium point or a sliding segment. We provide lower bounds for the local cyclicity for planar piecewise polynomial systems, M-c(p)(n), with degrees 2, 3, 4, and 5. More concretely, Mc p (2) >= 13, M-c(p) (3) >= 26, M-c(p) (4) >= 40, and M-c(p) (5) >= 58. The computations use parallelization algorithms. (C) 2020 Elsevier Ltd. All rights reserved.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-25T12:41:24Z
2021-06-25T12:41:24Z
2021-08-01
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.nonrwa.2020.103278
Nonlinear Analysis-real World Applications. Oxford: Pergamon-elsevier Science Ltd, v. 60, 19 p., 2021.
1468-1218
http://hdl.handle.net/11449/210159
10.1016/j.nonrwa.2020.103278
WOS:000633361700001
url http://dx.doi.org/10.1016/j.nonrwa.2020.103278
http://hdl.handle.net/11449/210159
identifier_str_mv Nonlinear Analysis-real World Applications. Oxford: Pergamon-elsevier Science Ltd, v. 60, 19 p., 2021.
1468-1218
10.1016/j.nonrwa.2020.103278
WOS:000633361700001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Analysis-real World Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Web of Science
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_ 1808129491756646400

Registros relacionados