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CLC number: TP183

On-line Access: 2008-01-10

Received: 2007-06-23

Revision Accepted: 2007-11-26

Crosschecked: 0000-00-00

Cited: 6

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Citations:  Bibtex RefMan EndNote GB/T7714

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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.2 P.262-270


Exponential synchronization of general chaotic delayed neural networks via hybrid feedback

Author(s):  Mei-qin LIU, Jian-hai ZHANG

Affiliation(s):  School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   liumeiqin@cee.zju.edu.cn, zjuzjh@gmail.com

Key Words:  Exponential synchronization, Hybrid feedback, Drive-response conception, Linear matrix inequality (LMI), Chaotic neural network model

Mei-qin LIU, Jian-hai ZHANG. Exponential synchronization of general chaotic delayed neural networks via hybrid feedback[J]. Journal of Zhejiang University Science A, 2008, 9(2): 262-270.

@article{title="Exponential synchronization of general chaotic delayed neural networks via hybrid feedback",
author="Mei-qin LIU, Jian-hai ZHANG",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Exponential synchronization of general chaotic delayed neural networks via hybrid feedback
%A Mei-qin LIU
%A Jian-hai ZHANG
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 2
%P 262-270
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A071336

T1 - Exponential synchronization of general chaotic delayed neural networks via hybrid feedback
A1 - Mei-qin LIU
A1 - Jian-hai ZHANG
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 2
SP - 262
EP - 270
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A071336

This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, and covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, recurrent multilayer perceptrons (RMLPs). By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) technique, some exponential synchronization criteria are derived. Using the drive-response concept, hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria. Finally, detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Aihara, K., Takabe, T., Toyoda, M., 1990. Chaotic neural networks. Phys. Lett. A, 144(6-7):333-340.

[2] Barabanov, N.E., Prokhorov, D.V., 2002. Stability analysis of discrete-time recurrent neural networks. IEEE Trans. on Neural Networks, 13(2):292-303.

[3] Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in System and Control Theory. Society for Industrial Applied Mathematics (SIAM), Philadelphia, PA.

[4] Cao, J., Wang, J., 2005. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. on Circuits and Systems I, 52(2):417-426.

[5] Cheng, C.J., Liao, T.L., Hwang, C.C., 2005. Exponential synchronization of a class of chaotic neural network. Chaos, Solitons and Fractals, 24(1):197-206.

[6] Cohen, M.A., Grossberg, S., 1983. Absolute stability of global pattern formation and parallel memory storage by competitive neural network. IEEE Trans. on Systems, Man, and Cybernetics, 13(5):815-826.

[7] Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., 1995. LMI Control Toolbox—for Use with Matlab. The Math Works Inc., Natick, MA.

[8] Gilli, M., 1993. Strange attractors in delayed cellular neural networks. IEEE Trans. on Circuits and Systems I, 40(11):849-853.

[9] Han, S.K., Kurrer, C., Kuramoto, Y., 1995. Dephasing and bursting in coupled neural oscillators. Phys. Rev. Lett., 75(17):3190-3193.

[10] Kwok, T., Smith, K.A., 2000. Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework. Neural Networks, 13(7):731-744.

[11] Liao, X., Chen, G., 2003. Chaos synchronization of general Lur'e systems via time-delay feedback control. Int. J. Bifurcation and Chaos, 13(1):207-213.

[12] Liu, M.Q., 2006. Discrete-time delayed standard neural network model and its application. Sci. China Ser. FInf. Sci., 49(2):137-154.

[13] Liu, M.Q., 2007. Delayed standard neural network models for control systems. IEEE Trans. on Neural Networks, 18(5):1376-1391.

[14] Lu, H., Leeuwen, C.V., 2006. Synchronization of chaotic neural networks via output or state coupling. Chaos, Solitons and Fractals, 30(1):166-176.

[15] Lu, J., Cao, J., 2007. Synchronization-based approach for parameters identification in delayed chaotic neural network. Physica A: Statistical Mechanics and its Applications, 382(2):672-682.

[16] Milanovic, V., Zaghloul, M.E., 1996. Synchronization of chaotic neural networks and applications to communications. Int. J. Bifurcation and Chaos, 6(12B):2571-2585.

[17] Nesterov, Y., Nemirovsky, A., 1994. Interior Point Polynomial Methods in Convex Programming: Theory and Applications. Society for Industrial Applied Mathematics (SIAM), Philadelphia, PA.

[18] Pecora, L.M., Carroll, T.L., 1990. Synchronization in chaotic systems. Phys. Rev. Lett., 64(8):821-824.

[19] Sun, Y., Cao, J., 2007. Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation. Phys. Lett. A, 364(3-4):277-285.

[20] Sun, Y., Cao, J., Wang, Z., 2007. Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing, 70(13-15):2477-2485.

[21] Tan, Z., Ali, M.K., 2001. Associative memory using synchronization in a chaotic neural network. Int. J. Modern Phys. C, 12(1):19-29.

[22] Wang, X.F., Zhong, G.Q., Tang, K.S., Man, K.F., Liu, Z.F., 2001. Generating chaos in Chua’s circuit via time-delay feedback. IEEE Trans. on Circuits and Systems I, 48(9):1151-1156.

[23] Zhang, H., Xie, Y., Liu, D., 2006. Synchronization of a class of delayed chaotic neural networks with fully unknown parameters. Dynamics of Continuous, Discrete & Impulsive Systems, Series B: Applications & Algorithms, 13(2):297-308.

[24] Zhang, S.L., Liu, M.Q., 2005. LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks. J. Zhejiang Univ. Sci., 6A(1):32-37.

[25] Zhou, J., Chen, T., Xiang, L., 2006. Robust synchronization of delayed neural networks based on adaptive control and parameters identification. Chaos, Solitons and Fractals, 27(4):905-913.

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