Global asymptotic stability for neural network models with distributed delays

Bibliographic Details
Main Author: Oliveira, José J.
Publication Date: 2009
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/13164
Summary: 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/pdfhttps://hdl.handle.net/1822/13164eng0895-717710.1016/j.mcm.2009.02.002http://www.sciencedirect.cominfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-04-12T05:25:39Zoai:repositorium.sdum.uminho.pt:1822/13164Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T16:34:11.459163Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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 https://hdl.handle.net/1822/13164
url https://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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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