Chaos synchronization of coupled neurons via adaptive sliding mode control

Yan Qiu Che; Jiang Wang; Shi Gang Cui; Bin Deng; Xi Le Wei; Wai Lok Chan; Kai Ming Tsang

doi:10.1016/j.nonrwa.2011.05.020

Chaos synchronization of coupled neurons via adaptive sliding mode control

Yan Qiu Che, Jiang Wang, Shi Gang Cui, Bin Deng, Xi Le Wei, Wai Lok Chan, Kai Ming Tsang

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

In this paper, an adaptive neural network (NN) sliding mode controller (SMC) is proposed to realize the chaos synchronization of two gap junction coupled FitzHughNagumo (FHN) neurons under external electrical stimulation. The controller consists of a radial basis function (RBF) NN and an SMC. After the RBFNN approximating the uncertain nonlinear part of the error dynamical system, the SMC realizes the desired control property regardless of the existence of the approximation errors and external disturbances. The weights of the NN are tuned online based on the sliding mode reaching law. According to the Lyapunov stability theory, the stability of the closed error system is guaranteed. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by the proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.

Original language	English (US)
Pages (from-to)	3199-3206
Number of pages	8
Journal	Nonlinear Analysis: Real World Applications
Volume	12
Issue number	6
DOIs	https://doi.org/10.1016/j.nonrwa.2011.05.020
State	Published - Dec 2011

All Science Journal Classification (ASJC) codes

Analysis
General Engineering
Economics, Econometrics and Finance(all)
Computational Mathematics
Applied Mathematics

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10.1016/j.nonrwa.2011.05.020

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@article{496105b8ea6c494699eb22d69e49e00c,

title = "Chaos synchronization of coupled neurons via adaptive sliding mode control",

abstract = "In this paper, an adaptive neural network (NN) sliding mode controller (SMC) is proposed to realize the chaos synchronization of two gap junction coupled FitzHughNagumo (FHN) neurons under external electrical stimulation. The controller consists of a radial basis function (RBF) NN and an SMC. After the RBFNN approximating the uncertain nonlinear part of the error dynamical system, the SMC realizes the desired control property regardless of the existence of the approximation errors and external disturbances. The weights of the NN are tuned online based on the sliding mode reaching law. According to the Lyapunov stability theory, the stability of the closed error system is guaranteed. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by the proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.",

author = "Che, {Yan Qiu} and Jiang Wang and Cui, {Shi Gang} and Bin Deng and Wei, {Xi Le} and Chan, {Wai Lok} and Tsang, {Kai Ming}",

note = "Funding Information: This work is supported by The National Natural Science Foundation of China (Grants No. 50907044 , No. 61072012 , No. 50707020 , and No. 60901035 ), The National Science Foundation for Post-doctoral Scientists of China (Grants No. 20080430090 and No. 200902275 ), and Natural Science Foundation of Tianjin (No. 10JCYBJC07000 ). We also acknowledge the support of the Hong Kong Polytechnic University.",

year = "2011",

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doi = "10.1016/j.nonrwa.2011.05.020",

language = "English (US)",

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journal = "Nonlinear Analysis: Real World Applications",

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T1 - Chaos synchronization of coupled neurons via adaptive sliding mode control

AU - Che, Yan Qiu

AU - Wang, Jiang

AU - Cui, Shi Gang

AU - Deng, Bin

AU - Wei, Xi Le

AU - Chan, Wai Lok

AU - Tsang, Kai Ming

N1 - Funding Information: This work is supported by The National Natural Science Foundation of China (Grants No. 50907044 , No. 61072012 , No. 50707020 , and No. 60901035 ), The National Science Foundation for Post-doctoral Scientists of China (Grants No. 20080430090 and No. 200902275 ), and Natural Science Foundation of Tianjin (No. 10JCYBJC07000 ). We also acknowledge the support of the Hong Kong Polytechnic University.

PY - 2011/12

Y1 - 2011/12

N2 - In this paper, an adaptive neural network (NN) sliding mode controller (SMC) is proposed to realize the chaos synchronization of two gap junction coupled FitzHughNagumo (FHN) neurons under external electrical stimulation. The controller consists of a radial basis function (RBF) NN and an SMC. After the RBFNN approximating the uncertain nonlinear part of the error dynamical system, the SMC realizes the desired control property regardless of the existence of the approximation errors and external disturbances. The weights of the NN are tuned online based on the sliding mode reaching law. According to the Lyapunov stability theory, the stability of the closed error system is guaranteed. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by the proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.

AB - In this paper, an adaptive neural network (NN) sliding mode controller (SMC) is proposed to realize the chaos synchronization of two gap junction coupled FitzHughNagumo (FHN) neurons under external electrical stimulation. The controller consists of a radial basis function (RBF) NN and an SMC. After the RBFNN approximating the uncertain nonlinear part of the error dynamical system, the SMC realizes the desired control property regardless of the existence of the approximation errors and external disturbances. The weights of the NN are tuned online based on the sliding mode reaching law. According to the Lyapunov stability theory, the stability of the closed error system is guaranteed. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by the proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.

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JO - Nonlinear Analysis: Real World Applications

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ER -

Chaos synchronization of coupled neurons via adaptive sliding mode control

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