Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line

In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain aga...

Descripción completa

Detalles Bibliográficos
Autores: Bastos, J.L.R., Buzzi, C.A., Torregrosa, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/536854
Acceso en línea:http://hdl.handle.net/2072/536854
Access Level:acceso abierto
Palabra clave:Center-focus problem
Local cyclicity
Nonsmooth boundary
Piecewise linear planar vector fields
id ES_f89b4a5ea2b03453340e3ffa728da23d
oai_identifier_str oai:recercat.cat:2072/536854
network_acronym_str ES
network_name_str España
repository_id_str
spelling Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching LineBastos, J.L.R.Buzzi, C.A.Torregrosa, J.Center-focus problemLocal cyclicityNonsmooth boundaryPiecewise linear planar vector fieldsIn this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type. © 2023, The Author(s).This work has been realized thanks to the Spanish Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación PID2019-104658GB-I00 grant; the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R &D CEX2020-001084-M grant; the Catalan AGAUR 2021SGR00113 grant; the Brazilian CNPq 304798/2019-3 and São Paulo Paulo Research Foundation (FAPESP), 2019/10269-3 grants; and the European Community H2020-MSCA-RISE-2017-777911 grant.Springer (Birkhauser)2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion11 p.application/pdfhttp://hdl.handle.net/2072/536854RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésQualitative Theory of Dynamical SystemsL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5368542026-05-29T05:05:01Z
dc.title.none.fl_str_mv Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
title Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
spellingShingle Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
Bastos, J.L.R.
Center-focus problem
Local cyclicity
Nonsmooth boundary
Piecewise linear planar vector fields
title_short Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
title_full Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
title_fullStr Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
title_full_unstemmed Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
title_sort Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
dc.creator.none.fl_str_mv Bastos, J.L.R.
Buzzi, C.A.
Torregrosa, J.
author Bastos, J.L.R.
author_facet Bastos, J.L.R.
Buzzi, C.A.
Torregrosa, J.
author_role author
author2 Buzzi, C.A.
Torregrosa, J.
author2_role author
author
dc.subject.none.fl_str_mv Center-focus problem
Local cyclicity
Nonsmooth boundary
Piecewise linear planar vector fields
topic Center-focus problem
Local cyclicity
Nonsmooth boundary
Piecewise linear planar vector fields
description In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type. © 2023, The Author(s).
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/536854
url http://hdl.handle.net/2072/536854
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Qualitative Theory of Dynamical Systems
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 11 p.
application/pdf
dc.publisher.none.fl_str_mv Springer (Birkhauser)
publisher.none.fl_str_mv Springer (Birkhauser)
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869425017412911104
score 15,812429

Similares en LA Referencia