Piecewise holomorphic systems
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jde.2022.05.027 http://hdl.handle.net/11449/240274 |
Resumo: | Holomorphic systems are well known in the literature due to their important properties: reversibility, integrability, non-existence of limit cycles and complete knowledge of the phase portraits around their non-essential singularities. In this paper we are concerned about studying the piecewise holomorphic systems (PWHS). Specifically, we study the sewing, sliding, and tangential regions of the PWHS and we classify the typical singularities of these systems. Also, we are interested in understanding how the trajectories of the regularized system associated with the PWHS transit through the region of regularization. In addition, we know that holomorphic systems have no limit cycles, but piecewise holomorphic systems do, so we provide conditions to ensure the existence of limit cycles of these systems. Additional conditions are provided to guarantee the stability and uniqueness of such limit cycles. |
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Piecewise holomorphic systemsLimit cyclesPiecewise holomorphic systemsRegularizationHolomorphic systems are well known in the literature due to their important properties: reversibility, integrability, non-existence of limit cycles and complete knowledge of the phase portraits around their non-essential singularities. In this paper we are concerned about studying the piecewise holomorphic systems (PWHS). Specifically, we study the sewing, sliding, and tangential regions of the PWHS and we classify the typical singularities of these systems. Also, we are interested in understanding how the trajectories of the regularized system associated with the PWHS transit through the region of regularization. In addition, we know that holomorphic systems have no limit cycles, but piecewise holomorphic systems do, so we provide conditions to ensure the existence of limit cycles of these systems. Additional conditions are provided to guarantee the stability and uniqueness of such limit cycles.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)São Paulo State University (Unesp) Institute of Biosciences Humanities and Exact Sciences, Rua C. Colombo, 2265São Paulo State University (Unesp) Institute of Biosciences Humanities and Exact Sciences, Rua C. Colombo, 2265FAPESP: 2019/10269-3FAPESP: 2020/04717-0FAPESP: 2020/06708-9CAPES: 88881.310741/2018-01CAPES: 88887.310463/2018-00Universidade Estadual Paulista (UNESP)Gouveia, Luiz F.S. [UNESP]Rondón, Gabriel [UNESP]Silva, Paulo R. da [UNESP]2023-03-01T20:09:36Z2023-03-01T20:09:36Z2022-09-25info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article440-472http://dx.doi.org/10.1016/j.jde.2022.05.027Journal of Differential Equations, v. 332, p. 440-472.1090-27320022-0396http://hdl.handle.net/11449/24027410.1016/j.jde.2022.05.0272-s2.0-85132217725Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Differential Equationsinfo:eu-repo/semantics/openAccess2023-03-01T20:09:36Zoai:repositorio.unesp.br:11449/240274Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:05:03.359695Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Piecewise holomorphic systems |
title |
Piecewise holomorphic systems |
spellingShingle |
Piecewise holomorphic systems Gouveia, Luiz F.S. [UNESP] Limit cycles Piecewise holomorphic systems Regularization |
title_short |
Piecewise holomorphic systems |
title_full |
Piecewise holomorphic systems |
title_fullStr |
Piecewise holomorphic systems |
title_full_unstemmed |
Piecewise holomorphic systems |
title_sort |
Piecewise holomorphic systems |
author |
Gouveia, Luiz F.S. [UNESP] |
author_facet |
Gouveia, Luiz F.S. [UNESP] Rondón, Gabriel [UNESP] Silva, Paulo R. da [UNESP] |
author_role |
author |
author2 |
Rondón, Gabriel [UNESP] Silva, Paulo R. da [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Gouveia, Luiz F.S. [UNESP] Rondón, Gabriel [UNESP] Silva, Paulo R. da [UNESP] |
dc.subject.por.fl_str_mv |
Limit cycles Piecewise holomorphic systems Regularization |
topic |
Limit cycles Piecewise holomorphic systems Regularization |
description |
Holomorphic systems are well known in the literature due to their important properties: reversibility, integrability, non-existence of limit cycles and complete knowledge of the phase portraits around their non-essential singularities. In this paper we are concerned about studying the piecewise holomorphic systems (PWHS). Specifically, we study the sewing, sliding, and tangential regions of the PWHS and we classify the typical singularities of these systems. Also, we are interested in understanding how the trajectories of the regularized system associated with the PWHS transit through the region of regularization. In addition, we know that holomorphic systems have no limit cycles, but piecewise holomorphic systems do, so we provide conditions to ensure the existence of limit cycles of these systems. Additional conditions are provided to guarantee the stability and uniqueness of such limit cycles. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-09-25 2023-03-01T20:09:36Z 2023-03-01T20:09:36Z |
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.jde.2022.05.027 Journal of Differential Equations, v. 332, p. 440-472. 1090-2732 0022-0396 http://hdl.handle.net/11449/240274 10.1016/j.jde.2022.05.027 2-s2.0-85132217725 |
url |
http://dx.doi.org/10.1016/j.jde.2022.05.027 http://hdl.handle.net/11449/240274 |
identifier_str_mv |
Journal of Differential Equations, v. 332, p. 440-472. 1090-2732 0022-0396 10.1016/j.jde.2022.05.027 2-s2.0-85132217725 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Differential Equations |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
440-472 |
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_ |
1808129488666492928 |