Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise

In this paper, two problems related to FitzHugh-Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise. We obtain a new result ensuring that such a system approximates the cor...

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Autores: Yang, Shuang, Li, Yangrong, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/143019
Acceso en línea:https://hdl.handle.net/11441/143019
https://doi.org/10.1063/5.0125383
Access Level:acceso abierto
Palabra clave:Random delay lattice system
FitzHugh-Nagumo system
Nonlinear Wong-Zakai noise
Pullback random attractor
Upper semicontinuity
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spelling Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noiseYang, ShuangLi, YangrongCaraballo Garrido, TomásRandom delay lattice systemFitzHugh-Nagumo systemNonlinear Wong-Zakai noisePullback random attractorUpper semicontinuityIn this paper, two problems related to FitzHugh-Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise. We obtain a new result ensuring that such a system approximates the corresponding deterministic system when the correlation time of Wong-Zakai noise goes to infinity rather than to zero. We first prove the existence of tempered random attractors for the random delayed lattice systems with a nonlinear drift function and a nonlinear diffusion term. The pullback asymptotic compactness of solutions is proved thanks to the Ascoli-Arzel`a theorem and uniform tailestimates. We then show that the upper semi-continuous of attractors as the correlation time tends to infinity. As for the second problem, we consider the corresponding deterministic version of the previous model, and study the convergence of attractors when the delay approaches zero. Namely, the upper semicontinuity of attractors for the delayed system to the non-delayed one is proved.AIP PublishingEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/143019https://doi.org/10.1063/5.0125383reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Mathematical Physics, 63, 111512-1.https://doi.org/10.1063/5.0125383info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1430192026-06-17T12:51:07Z
dc.title.none.fl_str_mv Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
title Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
spellingShingle Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
Yang, Shuang
Random delay lattice system
FitzHugh-Nagumo system
Nonlinear Wong-Zakai noise
Pullback random attractor
Upper semicontinuity
title_short Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
title_full Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
title_fullStr Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
title_full_unstemmed Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
title_sort Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise
dc.creator.none.fl_str_mv Yang, Shuang
Li, Yangrong
Caraballo Garrido, Tomás
author Yang, Shuang
author_facet Yang, Shuang
Li, Yangrong
Caraballo Garrido, Tomás
author_role author
author2 Li, Yangrong
Caraballo Garrido, Tomás
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Random delay lattice system
FitzHugh-Nagumo system
Nonlinear Wong-Zakai noise
Pullback random attractor
Upper semicontinuity
topic Random delay lattice system
FitzHugh-Nagumo system
Nonlinear Wong-Zakai noise
Pullback random attractor
Upper semicontinuity
description In this paper, two problems related to FitzHugh-Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise. We obtain a new result ensuring that such a system approximates the corresponding deterministic system when the correlation time of Wong-Zakai noise goes to infinity rather than to zero. We first prove the existence of tempered random attractors for the random delayed lattice systems with a nonlinear drift function and a nonlinear diffusion term. The pullback asymptotic compactness of solutions is proved thanks to the Ascoli-Arzel`a theorem and uniform tailestimates. We then show that the upper semi-continuous of attractors as the correlation time tends to infinity. As for the second problem, we consider the corresponding deterministic version of the previous model, and study the convergence of attractors when the delay approaches zero. Namely, the upper semicontinuity of attractors for the delayed system to the non-delayed one is proved.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/143019
https://doi.org/10.1063/5.0125383
url https://hdl.handle.net/11441/143019
https://doi.org/10.1063/5.0125383
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Mathematical Physics, 63, 111512-1.
https://doi.org/10.1063/5.0125383
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 AIP Publishing
publisher.none.fl_str_mv AIP Publishing
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 15,300719

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