Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems

We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the...

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Autores: Aragão Costa, Eder Ritis, Carvalho, Alexandre Nolasco, Marín Rubio, Pedro, Planas, Gabriela
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/84122
Acceso en línea:https://hdl.handle.net/11441/84122
Access Level:acceso abierto
Palabra clave:Dynamical system
Nonlinear semigroup
Attractor
Gradient-like semigroup
Łojasiewicz-Simon inequality
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spelling Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systemsAragão Costa, Eder RitisCarvalho, Alexandre NolascoMarín Rubio, PedroPlanas, GabrielaDynamical systemNonlinear semigroupAttractorGradient-like semigroupŁojasiewicz-Simon inequalityWe consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Lojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.Fundação de Amparo à Pesquisa do Estado de São PauloConselho Nacional de Desenvolvimento Científico e TecnológicoCoordenação de aperfeiçoamento de pessoal de nivel superiorMinisterio de Ciencia e InnovaciónJunta de AndalucíaMinisterio de EducaciónNicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear StudiesEcuaciones Diferenciales y Análisis NuméricoFQM-314: Análisis Estocástico de Sistemas Diferenciales2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/84122reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésTopological Methods in Nonlinear Analysis, 42 (2), 345-376.2008/50248-0305230/2011-5238/20112008/55516-3MTM2008-00088P07-FQM-02468PHB2010-0002-PC302865/2012-82008/09342-3https://projecteuclid.org/download/pdf_1/euclid.tmna/1461248983info:eu-repo/semantics/openAccessoai:idus.us.es:11441/841222026-06-17T12:51:07Z
dc.title.none.fl_str_mv Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
title Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
spellingShingle Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
Aragão Costa, Eder Ritis
Dynamical system
Nonlinear semigroup
Attractor
Gradient-like semigroup
Łojasiewicz-Simon inequality
title_short Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
title_full Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
title_fullStr Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
title_full_unstemmed Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
title_sort Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems
dc.creator.none.fl_str_mv Aragão Costa, Eder Ritis
Carvalho, Alexandre Nolasco
Marín Rubio, Pedro
Planas, Gabriela
author Aragão Costa, Eder Ritis
author_facet Aragão Costa, Eder Ritis
Carvalho, Alexandre Nolasco
Marín Rubio, Pedro
Planas, Gabriela
author_role author
author2 Carvalho, Alexandre Nolasco
Marín Rubio, Pedro
Planas, Gabriela
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM-314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Dynamical system
Nonlinear semigroup
Attractor
Gradient-like semigroup
Łojasiewicz-Simon inequality
topic Dynamical system
Nonlinear semigroup
Attractor
Gradient-like semigroup
Łojasiewicz-Simon inequality
description We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from −∞ and goes to ∞ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Lojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/84122
url https://hdl.handle.net/11441/84122
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Topological Methods in Nonlinear Analysis, 42 (2), 345-376.
2008/50248-0
305230/2011-5
238/2011
2008/55516-3
MTM2008-00088
P07-FQM-02468
PHB2010-0002-PC
302865/2012-8
2008/09342-3
https://projecteuclid.org/download/pdf_1/euclid.tmna/1461248983
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 Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies
publisher.none.fl_str_mv Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies
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 15,301603

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