Saddle-node of limit cycles in planar piecewise linear systems and applications

In this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of...

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Autores: Carmona Centeno, Victoriano, Fernández García, Soledad, Teruel, Antonio E.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/154287
Acceso en línea:https://hdl.handle.net/11441/154287
https://doi.org/10.3934/dcds.2019215
Access Level:acceso abierto
Palabra clave:Piecewise linear systems
Bifurcations
Saddle-node of limit cycles
Neuroscience
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spelling Saddle-node of limit cycles in planar piecewise linear systems and applicationsCarmona Centeno, VictorianoFernández García, SoledadTeruel, Antonio E.Piecewise linear systemsBifurcationsSaddle-node of limit cyclesNeuroscienceIn this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of the relation between the parameters of the system, such that the saddle-node bifurcation takes place, as well as of the period and amplitude of the non-hyperbolic limit cycle that bifurcates. We consider two applications, first a piecewise linear version of the FitzHugh-Nagumo neuron model of spike generation and second an electronic circuit, the memristor oscillator.American Institute of Mathematical Sciences (AIMS)Matemática Aplicada IIEcuaciones Diferenciales y Análisis NuméricoTIC130: Investigación en Sistemas Dinámicos en IngenieríaFQM120: Modelado Matemático y Simulación de Sistemas MedioambientalesMinisterio de Economía y Competitividad through the project MTM2015-65608-PJunta de Andaucía by project P12-FQM-1658University of Seville VPPI-US and partially supported by Ministerio de Economía y Competitividad through the project MTM2015-65608-PJunta de Andaucía by project P12-FQM-16582019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/154287https://doi.org/10.3934/dcds.2019215reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems, 39 (9), 5275-5299.MTM2015-65608-PP12-FQM-1658MTM2015-65608-PP12-FQM-1658https://www.aimsciences.org/article/doi/10.3934/dcds.2019215info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1542872026-06-17T12:51:07Z
dc.title.none.fl_str_mv Saddle-node of limit cycles in planar piecewise linear systems and applications
title Saddle-node of limit cycles in planar piecewise linear systems and applications
spellingShingle Saddle-node of limit cycles in planar piecewise linear systems and applications
Carmona Centeno, Victoriano
Piecewise linear systems
Bifurcations
Saddle-node of limit cycles
Neuroscience
title_short Saddle-node of limit cycles in planar piecewise linear systems and applications
title_full Saddle-node of limit cycles in planar piecewise linear systems and applications
title_fullStr Saddle-node of limit cycles in planar piecewise linear systems and applications
title_full_unstemmed Saddle-node of limit cycles in planar piecewise linear systems and applications
title_sort Saddle-node of limit cycles in planar piecewise linear systems and applications
dc.creator.none.fl_str_mv Carmona Centeno, Victoriano
Fernández García, Soledad
Teruel, Antonio E.
author Carmona Centeno, Victoriano
author_facet Carmona Centeno, Victoriano
Fernández García, Soledad
Teruel, Antonio E.
author_role author
author2 Fernández García, Soledad
Teruel, Antonio E.
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
Ecuaciones Diferenciales y Análisis Numérico
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
Ministerio de Economía y Competitividad through the project MTM2015-65608-P
Junta de Andaucía by project P12-FQM-1658
University of Seville VPPI-US and partially supported by Ministerio de Economía y Competitividad through the project MTM2015-65608-P
Junta de Andaucía by project P12-FQM-1658
dc.subject.none.fl_str_mv Piecewise linear systems
Bifurcations
Saddle-node of limit cycles
Neuroscience
topic Piecewise linear systems
Bifurcations
Saddle-node of limit cycles
Neuroscience
description In this article, we prove the existence of a saddle-node bifurcation of limit cycles in continuous piecewise linear systems with three zones. The bifurcation arises from the perturbation of a non-generic situation, where there exists a linear center in the middle zone. We obtain an approximation of the relation between the parameters of the system, such that the saddle-node bifurcation takes place, as well as of the period and amplitude of the non-hyperbolic limit cycle that bifurcates. We consider two applications, first a piecewise linear version of the FitzHugh-Nagumo neuron model of spike generation and second an electronic circuit, the memristor oscillator.
publishDate 2019
dc.date.none.fl_str_mv 2019
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 https://hdl.handle.net/11441/154287
https://doi.org/10.3934/dcds.2019215
url https://hdl.handle.net/11441/154287
https://doi.org/10.3934/dcds.2019215
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems, 39 (9), 5275-5299.
MTM2015-65608-P
P12-FQM-1658
MTM2015-65608-P
P12-FQM-1658
https://www.aimsciences.org/article/doi/10.3934/dcds.2019215
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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