Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations

The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The c...

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Autores: Caraballo Garrido, Tomás, Langa Rosado, José Antonio, Obaya García, Rafael
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/58657
Acceso en línea:http://hdl.handle.net/11441/58657
https://doi.org/10.1088/1361-6544/30/1/274
Access Level:acceso abierto
Palabra clave:Global attractor
Pullback attractor
Forward attractor
1D non-autonomous linear differential equation
Chaotic behavior in Li-Yorke sense
Chaotic behavior in Auslander-Yorke sense
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spelling Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equationsCaraballo Garrido, TomásLanga Rosado, José AntonioObaya García, RafaelGlobal attractorPullback attractorForward attractor1D non-autonomous linear differential equationChaotic behavior in Li-Yorke senseChaotic behavior in Auslander-Yorke senseThe global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The continuity of the cocycle attractor in the parameter is usually a difficult question. In this paper we develop in detail a 1D non-autonomous linear differential equation and show the richness of non-autonomous dynamics by focusing on the continuity, characterization and chaotic dynamics of the cocycle attractors. In particular, we analyse the sets of continuity and discontinuity for the parameter of the attractors, and relate them with the eventually forward behaviour of the processes. We will also find chaotic behaviour on the attractors in the Li-Yorke and Auslander-Yorke senses. Note that they hold for linear 1D equations, which shows a crucial difference with respect to the presence of chaotic dynamics in autonomous systems.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de AndalucíaBrazilian-European partnership in Dynamical Systems (BREUDS)Junta de Castilla y LeónIOP PublishingEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/58657https://doi.org/10.1088/1361-6544/30/1/274reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinearity, 30 (1), 274-299.info:eu-repo/grantAgreement/MINECO/MTM2015-63723-P/FQM-1492info:eu-repo/grantAgreement/MINECO/MTM2011-22411/info:eu-repo/grantAgreement/EC/FP7/318999info:eu-repo/grantAgreement/MINECO/MTM2012-30860/VA118A12-1http://iopscience.iop.org/article/10.1088/1361-6544/30/1/274/pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/586572026-06-17T12:51:07Z
dc.title.none.fl_str_mv Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
title Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
spellingShingle Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
Caraballo Garrido, Tomás
Global attractor
Pullback attractor
Forward attractor
1D non-autonomous linear differential equation
Chaotic behavior in Li-Yorke sense
Chaotic behavior in Auslander-Yorke sense
title_short Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
title_full Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
title_fullStr Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
title_full_unstemmed Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
title_sort Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Langa Rosado, José Antonio
Obaya García, Rafael
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Langa Rosado, José Antonio
Obaya García, Rafael
author_role author
author2 Langa Rosado, José Antonio
Obaya García, Rafael
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 Global attractor
Pullback attractor
Forward attractor
1D non-autonomous linear differential equation
Chaotic behavior in Li-Yorke sense
Chaotic behavior in Auslander-Yorke sense
topic Global attractor
Pullback attractor
Forward attractor
1D non-autonomous linear differential equation
Chaotic behavior in Li-Yorke sense
Chaotic behavior in Auslander-Yorke sense
description The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The continuity of the cocycle attractor in the parameter is usually a difficult question. In this paper we develop in detail a 1D non-autonomous linear differential equation and show the richness of non-autonomous dynamics by focusing on the continuity, characterization and chaotic dynamics of the cocycle attractors. In particular, we analyse the sets of continuity and discontinuity for the parameter of the attractors, and relate them with the eventually forward behaviour of the processes. We will also find chaotic behaviour on the attractors in the Li-Yorke and Auslander-Yorke senses. Note that they hold for linear 1D equations, which shows a crucial difference with respect to the presence of chaotic dynamics in autonomous systems.
publishDate 2017
dc.date.none.fl_str_mv 2017
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 http://hdl.handle.net/11441/58657
https://doi.org/10.1088/1361-6544/30/1/274
url http://hdl.handle.net/11441/58657
https://doi.org/10.1088/1361-6544/30/1/274
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinearity, 30 (1), 274-299.
info:eu-repo/grantAgreement/MINECO/MTM2015-63723-P/
FQM-1492
info:eu-repo/grantAgreement/MINECO/MTM2011-22411/
info:eu-repo/grantAgreement/EC/FP7/318999
info:eu-repo/grantAgreement/MINECO/MTM2012-30860/
VA118A12-1
http://iopscience.iop.org/article/10.1088/1361-6544/30/1/274/pdf
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 IOP Publishing
publisher.none.fl_str_mv IOP 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 15,300724

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