Global exponential stability of nonautonomous neural network models with unbounded delays

Bibliographic Details
Main Author: Oliveira, José J.
Publication Date: 2017
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/47159
Summary: For a nonautonomous class of n-dimensional di erential system with in nite delays, we give su cient conditions for its global exponential stability, without showing the existence of an equilibrium point, or a periodic solution, or an almost periodic solution. We apply our main result to several concrete neural network models, studied in the literature, and a comparison of results is given. Contrary to usual in the literature about neural networks, the assumption of bounded coe cients is not need to obtain the global exponential stability. Finally, we present numerical examples to illustrate the e ectiveness of our results.
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spelling Global exponential stability of nonautonomous neural network models with unbounded delaysCohen-Grossberg neural networksInfinite distributed delaysInfinite discrete delaysGlobal exponential stabilityUnbounded coefficientsCiências Naturais::MatemáticasScience & TechnologyFor a nonautonomous class of n-dimensional di erential system with in nite delays, we give su cient conditions for its global exponential stability, without showing the existence of an equilibrium point, or a periodic solution, or an almost periodic solution. We apply our main result to several concrete neural network models, studied in the literature, and a comparison of results is given. Contrary to usual in the literature about neural networks, the assumption of bounded coe cients is not need to obtain the global exponential stability. Finally, we present numerical examples to illustrate the e ectiveness of our results.The paper was supported by the Research Center of Mathematics of University of Minho with the Portuguese Funds from the FCT - “Fundação para a Ciência e a Tecnologia”, through the Project UID/MAT/00013/2013. The author thanks the referees for valuable comments.info:eu-repo/semantics/publishedVersionElsevierUniversidade do MinhoOliveira, José J.2017-122017-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/47159eng0893-608010.1016/j.neunet.2017.09.00628987978https://www.sciencedirect.com/science/article/pii/S0893608017302083info: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:RCAAP2025-04-12T04:29:46Zoai:repositorium.sdum.uminho.pt:1822/47159Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:15:39.541341Repositórios 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 exponential stability of nonautonomous neural network models with unbounded delays
title Global exponential stability of nonautonomous neural network models with unbounded delays
spellingShingle Global exponential stability of nonautonomous neural network models with unbounded delays
Oliveira, José J.
Cohen-Grossberg neural networks
Infinite distributed delays
Infinite discrete delays
Global exponential stability
Unbounded coefficients
Ciências Naturais::Matemáticas
Science & Technology
title_short Global exponential stability of nonautonomous neural network models with unbounded delays
title_full Global exponential stability of nonautonomous neural network models with unbounded delays
title_fullStr Global exponential stability of nonautonomous neural network models with unbounded delays
title_full_unstemmed Global exponential stability of nonautonomous neural network models with unbounded delays
title_sort Global exponential stability of nonautonomous neural network models with unbounded 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 Cohen-Grossberg neural networks
Infinite distributed delays
Infinite discrete delays
Global exponential stability
Unbounded coefficients
Ciências Naturais::Matemáticas
Science & Technology
topic Cohen-Grossberg neural networks
Infinite distributed delays
Infinite discrete delays
Global exponential stability
Unbounded coefficients
Ciências Naturais::Matemáticas
Science & Technology
description For a nonautonomous class of n-dimensional di erential system with in nite delays, we give su cient conditions for its global exponential stability, without showing the existence of an equilibrium point, or a periodic solution, or an almost periodic solution. We apply our main result to several concrete neural network models, studied in the literature, and a comparison of results is given. Contrary to usual in the literature about neural networks, the assumption of bounded coe cients is not need to obtain the global exponential stability. Finally, we present numerical examples to illustrate the e ectiveness of our results.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
2017-12-01T00:00:00Z
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/1822/47159
url https://hdl.handle.net/1822/47159
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0893-6080
10.1016/j.neunet.2017.09.006
28987978
https://www.sciencedirect.com/science/article/pii/S0893608017302083
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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