Limit cycles in planar piecewise linear differential systems with nonregular separation line
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.physd.2016.07.008 http://hdl.handle.net/11449/169076 |
Resumo: | In this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2π−α, respectively, for α∈(0,π). We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α, we prove the existence of systems with four limit cycles up to fifth order and, for α=π/2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line. |
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Repositório Institucional da UNESP |
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Limit cycles in planar piecewise linear differential systems with nonregular separation lineLimit cycle in Melnikov higher order perturbationNon-smooth differential systems in two zonesNonregular separation lineIn this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2π−α, respectively, for α∈(0,π). We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α, we prove the existence of systems with four limit cycles up to fifth order and, for α=π/2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Ag�ncia de Gesti� d'Ajuts Universitaris i de RecercaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Departamento de Matem�tica Faculdade de Engenharia de Ilha Solteira Universidade Estadual Paulista (UNESP), Rua Rio de Janeiro, 266, CEPDepartament de Matem�tiques Universitat Aut�noma de BarcelonaDepartamento de Matem�tica Faculdade de Engenharia de Ilha Solteira Universidade Estadual Paulista (UNESP), Rua Rio de Janeiro, 266, CEPFAPESP: 2013/24541-0Ag�ncia de Gesti� d'Ajuts Universitaris i de Recerca: 2014 SGR568CAPES: 88881.030454/2013-01Universidade Estadual Paulista (Unesp)Universitat Aut�noma de BarcelonaCardin, Pedro Toniol [UNESP]Torregrosa, Joan2018-12-11T16:44:21Z2018-12-11T16:44:21Z2016-12-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article67-82application/pdfhttp://dx.doi.org/10.1016/j.physd.2016.07.008Physica D: Nonlinear Phenomena, v. 337, p. 67-82.0167-2789http://hdl.handle.net/11449/16907610.1016/j.physd.2016.07.0082-s2.0-849939535242-s2.0-84993953524.pdf80328799159066610000-0002-8723-8200Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysica D: Nonlinear Phenomena0,861info:eu-repo/semantics/openAccess2023-10-06T06:07:08Zoai:repositorio.unesp.br:11449/169076Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:10:06.867727Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
title |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
spellingShingle |
Limit cycles in planar piecewise linear differential systems with nonregular separation line Cardin, Pedro Toniol [UNESP] Limit cycle in Melnikov higher order perturbation Non-smooth differential systems in two zones Nonregular separation line |
title_short |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
title_full |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
title_fullStr |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
title_full_unstemmed |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
title_sort |
Limit cycles in planar piecewise linear differential systems with nonregular separation line |
author |
Cardin, Pedro Toniol [UNESP] |
author_facet |
Cardin, Pedro Toniol [UNESP] Torregrosa, Joan |
author_role |
author |
author2 |
Torregrosa, Joan |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universitat Aut�noma de Barcelona |
dc.contributor.author.fl_str_mv |
Cardin, Pedro Toniol [UNESP] Torregrosa, Joan |
dc.subject.por.fl_str_mv |
Limit cycle in Melnikov higher order perturbation Non-smooth differential systems in two zones Nonregular separation line |
topic |
Limit cycle in Melnikov higher order perturbation Non-smooth differential systems in two zones Nonregular separation line |
description |
In this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2π−α, respectively, for α∈(0,π). We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α, we prove the existence of systems with four limit cycles up to fifth order and, for α=π/2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-12-15 2018-12-11T16:44:21Z 2018-12-11T16:44:21Z |
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.2016.07.008 Physica D: Nonlinear Phenomena, v. 337, p. 67-82. 0167-2789 http://hdl.handle.net/11449/169076 10.1016/j.physd.2016.07.008 2-s2.0-84993953524 2-s2.0-84993953524.pdf 8032879915906661 0000-0002-8723-8200 |
url |
http://dx.doi.org/10.1016/j.physd.2016.07.008 http://hdl.handle.net/11449/169076 |
identifier_str_mv |
Physica D: Nonlinear Phenomena, v. 337, p. 67-82. 0167-2789 10.1016/j.physd.2016.07.008 2-s2.0-84993953524 2-s2.0-84993953524.pdf 8032879915906661 0000-0002-8723-8200 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physica D: Nonlinear Phenomena 0,861 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
67-82 application/pdf |
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_ |
1808128327034077184 |