Global asymptotic stability for neural network models with distributed delays

Detalhes bibliográficos
Autor(a) principal: Oliveira, José J.
Data de Publicação: 2009
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/13164
Resumo: In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the nondelayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well known neural network models of Hopfield, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.
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spelling Global asymptotic stability for neural network models with distributed delaysDelayed neural network modelsDistributed delaysTime-varing delaysGlobal asymptotic stabilityM-matrixTime-varying delaysScience & TechnologyIn this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the nondelayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well known neural network models of Hopfield, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.Fundação para a Ciência e a Tecnologia (FCT)ElsevierUniversidade do MinhoOliveira, José J.2009-072009-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/13164eng0895-717710.1016/j.mcm.2009.02.002http://www.sciencedirect.cominfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:53:47Zoai:repositorium.sdum.uminho.pt:1822/13164Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:53:15.695449Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Global asymptotic stability for neural network models with distributed delays
title Global asymptotic stability for neural network models with distributed delays
spellingShingle Global asymptotic stability for neural network models with distributed delays
Oliveira, José J.
Delayed neural network models
Distributed delays
Time-varing delays
Global asymptotic stability
M-matrix
Time-varying delays
Science & Technology
title_short Global asymptotic stability for neural network models with distributed delays
title_full Global asymptotic stability for neural network models with distributed delays
title_fullStr Global asymptotic stability for neural network models with distributed delays
title_full_unstemmed Global asymptotic stability for neural network models with distributed delays
title_sort Global asymptotic stability for neural network models with distributed delays
author Oliveira, José J.
author_facet Oliveira, José J.
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Oliveira, José J.
dc.subject.por.fl_str_mv Delayed neural network models
Distributed delays
Time-varing delays
Global asymptotic stability
M-matrix
Time-varying delays
Science & Technology
topic Delayed neural network models
Distributed delays
Time-varing delays
Global asymptotic stability
M-matrix
Time-varying delays
Science & Technology
description In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the nondelayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well known neural network models of Hopfield, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.
publishDate 2009
dc.date.none.fl_str_mv 2009-07
2009-07-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/13164
url http://hdl.handle.net/1822/13164
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0895-7177
10.1016/j.mcm.2009.02.002
http://www.sciencedirect.com
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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