Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms

Detalhes bibliográficos
Autor(a) principal: Bento, António
Data de Publicação: 2023
Outros Autores: Oliveira, José J., Silva, César
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/85949
Resumo: In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincar\'e map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory(BAM).
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spelling Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage termsNonlinear delay difference equationExponential stabilityPeriodic solutionLeakage delayNeural networksCiências Naturais::MatemáticasIn this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincar\'e map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory(BAM).CMA-UBI -Centro de Matemática e Aplicações da Universidade da Beira Interior(UIDB/00212/2020)ElsevierUniversidade do MinhoBento, AntónioOliveira, José J.Silva, César2023-07-172025-07-17T00:00:00Z2023-07-17T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/85949engBento, A. J. G., Oliveira, J. J., & Silva, C. M. (2023, November). Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms. Communications in Nonlinear Science and Numerical Simulation. Elsevier BV. http://doi.org/10.1016/j.cnsns.2023.1074291007-57041878-727410.1016/j.cnsns.2023.107429107429https://www.sciencedirect.com/science/article/pii/S1007570423003477info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-12T01:18:06Zoai:repositorium.sdum.uminho.pt:1822/85949Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:26:18.234460Repositório 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 Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
title Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
spellingShingle Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
Bento, António
Nonlinear delay difference equation
Exponential stability
Periodic solution
Leakage delay
Neural networks
Ciências Naturais::Matemáticas
title_short Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
title_full Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
title_fullStr Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
title_full_unstemmed Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
title_sort Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
author Bento, António
author_facet Bento, António
Oliveira, José J.
Silva, César
author_role author
author2 Oliveira, José J.
Silva, César
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Bento, António
Oliveira, José J.
Silva, César
dc.subject.por.fl_str_mv Nonlinear delay difference equation
Exponential stability
Periodic solution
Leakage delay
Neural networks
Ciências Naturais::Matemáticas
topic Nonlinear delay difference equation
Exponential stability
Periodic solution
Leakage delay
Neural networks
Ciências Naturais::Matemáticas
description In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincar\'e map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory(BAM).
publishDate 2023
dc.date.none.fl_str_mv 2023-07-17
2023-07-17T00:00:00Z
2025-07-17T00:00:00Z
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/1822/85949
url https://hdl.handle.net/1822/85949
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bento, A. J. G., Oliveira, J. J., & Silva, C. M. (2023, November). Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms. Communications in Nonlinear Science and Numerical Simulation. Elsevier BV. http://doi.org/10.1016/j.cnsns.2023.107429
1007-5704
1878-7274
10.1016/j.cnsns.2023.107429
107429
https://www.sciencedirect.com/science/article/pii/S1007570423003477
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
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
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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
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