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Exponential synchronization of neural networks with time-varying delays. (English) Zbl 1173.34349
Summary: We study the problem of exponential synchronization of a class of neural networks with time-varying delays. By utilizing the Lyapunov functional method and combining it with linear matrix inequality approach, we obtain the exponential synchronization of the derive-response structure of neural networks. Some sufficient conditions for the exponential synchronization of neural networks are given in terms of the feasible solution to the LMIs, which can be solved by various convex optimization algorithms. A numerical example is given to illustrate the proposed theory.

34K25Asymptotic theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
Full Text: DOI
[1] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems. Phys. lett. 64, No. 8, 821-824 (1990) · Zbl 0938.37019
[2] Chen, G.; Dong, X.: From chaos to order-perspectives, methodologies and applications. (1998) · Zbl 0908.93005
[3] Chen, F. X.; Zhang, W. D.: LMI criteria for robust chaos synchronization of a class of chaotic systems. Nonlinear anal. (2006)
[4] Jiang, G. P.; Tang, K. S.; Chen, G.: A simple global synchronization criterion for couples chaotic systems. Chaos solitons fractals 15, 925-935 (2003) · Zbl 1065.70015
[5] Yu, H.; Liu, Y.: Chaotic synchronization based on stability criterion of linear systems. Phys. lett. A. 314, 292-298 (2003) · Zbl 1026.37024
[6] Liu, F.; Ren, Y.; Shen, X.; Qiu, Z.: A linear feedback synchronization theorem for a class of chaotic systems. Chaos solitons fractals 13, No. 4, 723-730 (2002) · Zbl 1032.34045
[7] Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos solitons fractals 18, 141-148 (2003) · Zbl 1048.93508
[8] Arik, S.: Global asymptotic stability of a lager class of neural networks with constant time delays. Phys. lett. A 311, 504-511 (2003) · Zbl 1098.92501
[9] Joy, M.: On the global convergence of a class of functional differential equations with applications in neural networks theory. J. math. Anal. appl. 232, 61-81 (1999) · Zbl 0958.34057
[10] Gilli, M.: Strange attractors in delayed cellular neural networks. IEEE trans. Circuits syst. I. 40, No. 11, 849-853 (1993) · Zbl 0844.58056
[11] Lu, H. T.: Chaotic attractors in delayed neural networks. Phys. lett. A 298, 109-116 (2002) · Zbl 0995.92004
[12] He, G.; Cao, Z.; Zhu, P.; Ogura, H.: Controlling chaos in a chaotic neural network. Neural netw. 16, No. 8, 1195-1200 (2003)
[13] Yu, H.; Liu, Y.; Peng, J. J.: Control of chaotic neural networks based on contraction mappings. Chaos solitons fractals 22, No. 4, 787-792 (2004) · Zbl 1060.93537
[14] Chen, G.; Zhou, J.; Liu, Z.: Global synchronization of coupled delayed neural networks and application to chaotic CNN models. Internat J. Bifur. chaos 14, No. 7, 2229-2240 (2004) · Zbl 1077.37506
[15] Ch, Chao Jung; The-Luliao; Yan, Jun-Juh; Hwang, Chi-Chuan: Exponential synchronization of a class of neural networks with time-varying delays, syst. Man cybernetics-part B. Cybernetics. 36, No. 1, 209-215 (2006)
[16] Khalil, H. K.: Nonlinear systems. (1992) · Zbl 0969.34001
[17] Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay systems. (2003) · Zbl 1039.34067