Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control
The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activa...
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Series: | Discrete Dynamics in Nature and Society |
Online Access: | http://dx.doi.org/10.1155/2013/147164 |
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doaj-a7e829c6d7904b5fb16777c434ca306f2020-11-24T22:39:17ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/147164147164Synchronization of Discontinuous Neural Networks with Delays via Adaptive ControlXinsong Yang0Jinde Cao1Department of Mathematics, Chongqing Normal University, Chongqing 401331, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaThe drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control.http://dx.doi.org/10.1155/2013/147164 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xinsong Yang Jinde Cao |
spellingShingle |
Xinsong Yang Jinde Cao Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control Discrete Dynamics in Nature and Society |
author_facet |
Xinsong Yang Jinde Cao |
author_sort |
Xinsong Yang |
title |
Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control |
title_short |
Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control |
title_full |
Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control |
title_fullStr |
Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control |
title_full_unstemmed |
Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control |
title_sort |
synchronization of discontinuous neural networks with delays via adaptive control |
publisher |
Hindawi Limited |
series |
Discrete Dynamics in Nature and Society |
issn |
1026-0226 1607-887X |
publishDate |
2013-01-01 |
description |
The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control. |
url |
http://dx.doi.org/10.1155/2013/147164 |
work_keys_str_mv |
AT xinsongyang synchronizationofdiscontinuousneuralnetworkswithdelaysviaadaptivecontrol AT jindecao synchronizationofdiscontinuousneuralnetworkswithdelaysviaadaptivecontrol |
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1725709835756896256 |