Local cyclicity in low degree planar piecewise polynomial vector fields
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
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. |
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Repositório Institucional da UNESP |
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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 |