Piecewise holomorphic systems

Detalhes bibliográficos
Autor(a) principal: Gouveia, Luiz F.S. [UNESP]
Data de Publicação: 2022
Outros Autores: Rondón, Gabriel [UNESP], Silva, Paulo R. da [UNESP]
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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spelling 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
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