Synchronization of Caputo fractional neural networks with bounded time variable delays

Synchronization of Caputo fractional neural networks with bounded time variable delays

One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the jjth neuron to the iith neuron) are variable in time and unbounded. The rate of ch...

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Autores principales: Almeida Ricardo, Hristova Snezhana, Tersian Stepan
Formato: article
Lenguaje:EN
Publicado: De Gruyter 2021
Materias:
nonlinear neural networks
delay
synchronization
lyapunov functions
34-xx
39-xx
44-xx
Mathematics
QA1-939
Acceso en línea:https://doaj.org/article/37a9c892c506427d90a0e3dfed16b616
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spelling oai:doaj.org-article:37a9c892c506427d90a0e3dfed16b6162021-12-05T14:10:53ZSynchronization of Caputo fractional neural networks with bounded time variable delays2391-545510.1515/math-2021-0046https://doaj.org/article/37a9c892c506427d90a0e3dfed16b6162021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0046https://doaj.org/toc/2391-5455One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the jjth neuron to the iith neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.Almeida RicardoHristova SnezhanaTersian StepanDe Gruyterarticlenonlinear neural networksdelaysynchronizationlyapunov functions34-xx39-xx44-xxMathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 388-399 (2021)
institution DOAJ
collection DOAJ
language EN
topic nonlinear neural networks
delay
synchronization
lyapunov functions
34-xx
39-xx
44-xx
Mathematics
QA1-939
spellingShingle nonlinear neural networks
delay
synchronization
lyapunov functions
34-xx
39-xx
44-xx
Mathematics
QA1-939
Almeida Ricardo
Hristova Snezhana
Tersian Stepan
Synchronization of Caputo fractional neural networks with bounded time variable delays
description One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the jjth neuron to the iith neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.
format article
author Almeida Ricardo
Hristova Snezhana
Tersian Stepan
author_facet Almeida Ricardo
Hristova Snezhana
Tersian Stepan
author_sort Almeida Ricardo
title Synchronization of Caputo fractional neural networks with bounded time variable delays
title_short Synchronization of Caputo fractional neural networks with bounded time variable delays
title_full Synchronization of Caputo fractional neural networks with bounded time variable delays
title_fullStr Synchronization of Caputo fractional neural networks with bounded time variable delays
title_full_unstemmed Synchronization of Caputo fractional neural networks with bounded time variable delays
title_sort synchronization of caputo fractional neural networks with bounded time variable delays
publisher De Gruyter
publishDate 2021
url https://doaj.org/article/37a9c892c506427d90a0e3dfed16b616
work_keys_str_mv AT almeidaricardo synchronizationofcaputofractionalneuralnetworkswithboundedtimevariabledelays
AT hristovasnezhana synchronizationofcaputofractionalneuralnetworkswithboundedtimevariabledelays
AT tersianstepan synchronizationofcaputofractionalneuralnetworkswithboundedtimevariabledelays
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