Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , |
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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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 |
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info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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