Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapu...

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Main Authors: Zhiqiang Wang, Lili Wang, Rui Xu
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2017/6987436
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spelling doaj-f3c0a08b04594dc9971cde881cf3456b2020-11-25T00:18:27ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/69874366987436Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion TermsZhiqiang Wang0Lili Wang1Rui Xu2Institute of Applied Mathematics, Hebei Academy of Sciences, No. 46 South Youyi Street, Shijiazhuang 050081, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 West Heping Road, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 West Heping Road, Shijiazhuang 050003, ChinaWe study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.http://dx.doi.org/10.1155/2017/6987436
collection DOAJ
language English
format Article
sources DOAJ
author Zhiqiang Wang
Lili Wang
Rui Xu
spellingShingle Zhiqiang Wang
Lili Wang
Rui Xu
Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms
Mathematical Problems in Engineering
author_facet Zhiqiang Wang
Lili Wang
Rui Xu
author_sort Zhiqiang Wang
title Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms
title_short Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms
title_full Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms
title_fullStr Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms
title_full_unstemmed Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms
title_sort adaptive exponential synchronization for stochastic competitive neural networks with time-varying leakage delays and reaction-diffusion terms
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2017-01-01
description We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.
url http://dx.doi.org/10.1155/2017/6987436
work_keys_str_mv AT zhiqiangwang adaptiveexponentialsynchronizationforstochasticcompetitiveneuralnetworkswithtimevaryingleakagedelaysandreactiondiffusionterms
AT liliwang adaptiveexponentialsynchronizationforstochasticcompetitiveneuralnetworkswithtimevaryingleakagedelaysandreactiondiffusionterms
AT ruixu adaptiveexponentialsynchronizationforstochasticcompetitiveneuralnetworkswithtimevaryingleakagedelaysandreactiondiffusionterms
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