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Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms. (English) Zbl 1197.35148

Summary: This paper presents an exponential synchronization scheme for a class of neural networks with time-varying and distributed delays and reaction-diffusion terms. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory. At the same time, the update laws of parameters are proposed to guarantee the synchronization of delayed neural networks with all parameters unknown. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

35K57 Reaction-diffusion equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93D21 Adaptive or robust stabilization
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[1] Pecora, L. M.; Carrol, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 821-823 (1990)
[2] Pecora, L. M.; Carrol, T. L.; Johnson, G. A., Fundamentals of synchronization in chaotic systems, concepts, and applications, Chaos, 7, 4, 520-543 (1998) · Zbl 0933.37030
[3] Liu, B.; Liu, X.; Chen, G.; Wang, H., Robust impulsive synchronization of uncertain dynamical networks, IEEE Trans Circuits Syst I, 52, 1431-1441 (2005) · Zbl 1374.82016
[4] Khadra, A.; Liu, X.; Shen, X., Impulsively synchronizing chaotic systems with delay and applications to secure communication, Automatica, 41, 1491-1502 (2005) · Zbl 1086.93051
[5] Wang, Y.; Guan, Z.; Xiao, J., Impulsive control for synchronization of a class of continuous systems, Chaos, 14, 199-203 (2004)
[6] Hu, J.; Chen, S.; Chen, L., Adaptive control for anti-synchronization of chua’s chaotic system, Phys Lett A, 339, 455-460 (2005) · Zbl 1145.93366
[7] Sun, Y.; Cao, J., Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation, Phys Lett A, 364, 277-285 (2007) · Zbl 1203.93110
[8] Xiong, W.; Xie, W.; Cao, J., Adaptive exponential synchronization of delayed chaotic networks, Physica A, 370, 832-842 (2006)
[9] Sun, J., Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control, Chaos, Solitons & Fractals, 21, 143-150 (2004) · Zbl 1048.37509
[10] Cheng, C.; Liao, T.; Yan, J.; Hwang, C., Exponential synchronization of a class of neural networks with time-varying delays, IEEE Tran. Syst Man Cybern Part B: Cybern, 36, 1, 209-215 (2006)
[11] Cao, J.; Li, H.; Daniel, W., Synchronization criteria of Lure systems with time-delay feedback control, Chaos, Solitons & Fractals, 23, 4, 1285-1298 (2005) · Zbl 1086.93050
[12] Park, J., A novel criterion for delayed feedback control of time-delay chaotic systems, Chaos, Solitons & Fractals, 23, 2, 495-501 (2005) · Zbl 1061.93507
[13] Lou, X.; Cui, B., Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, J Math Anal Appl, 328, 316-326 (2007) · Zbl 1132.34061
[14] Zou, F.; Nossek, J. A., Bifurcation and chaos in cellular neural networks, IEEE Trans Circuit Syst I, 40, 3, 166-173 (1993) · Zbl 0782.92003
[15] Gilli, M., Strange attractors in delayed cellular neural networks, IEEE Trans Circuit Syst I, 40, 11, 849-853 (1993) · Zbl 0844.58056
[16] Lou, X.; Cui, B., Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays, IEEE Trans Syst Man Cybernet - Part B, 37, 3, 713-719 (2007)
[17] Lu, H. T., Chaotic attractors in delayed neural networks, Phys Lett A, 298, 109-116 (2002) · Zbl 0995.92004
[18] Lou, X.; Cui, B., Absolute exponential stability analysis of delayed bi-directional associative memory neural networks, Chaos, Solitons & Fractals, 31, 3, 695-701 (2007) · Zbl 1147.34358
[19] Chen, G.; Zhou, J.; Liu, Z., Global synchronization of coupled delayed neural networks with application to chaotic CNN models, Int J Bifurcat Chaos, 14, 2229-2240 (2004) · Zbl 1077.37506
[20] Lu, W.; Chen, T., Synchronization of coupled connected neural networks with delays, IEEE Trans Circuit Syst I, 51, 2491-2503 (2004) · Zbl 1371.34118
[21] Lu, H. T.; Van Leeuwen, C., Synchronization of chaotic neural networks via output or state coupling, Chaos, Solitons & Fractals, 30, 166-176 (2006) · Zbl 1144.37377
[22] Wang, Y.; Cao, J., Synchronization of a class of delayed neural networks with reaction-diffusion terms, Phys Lett A, 369, 3, 201-211 (2007)
[23] Song, Q. K.; Zhao, Z. J.; Li, Y. M., Global exponential stability of BAM with distributed delays and reaction-diffusion terms, Phys Lett A, 335, 213-225 (2005) · Zbl 1123.68347
[24] Lou, X.; Cui, B., Boundedness and exponential stability for nonautonomous cellular neural networks with reaction-diffusion terms, Chaos, Solitons & Fractals, 33, 2, 653-662 (2007) · Zbl 1133.35386
[25] Yuan, K.; Cao, J.; Li, H., Robust stability of switched Cohen-Grossberg neural networks with mixed time-varying delays, IEEE Trans Syst Man Cybernet - Part B, 36, 6, 1356-1363 (2006)
[26] Wang, Z.; Liu, Y.; Liu, X., On global asymptotic stability of neural networks with discrete and distributed delays, Phys Lett A, 345, 4-6, 299-308 (2005) · Zbl 1345.92017
[27] Chen, S. H.; Hu, J.; Wang, C. P.; Lü, J. H., Adaptive synchronization of uncertain Rössler hyperchaotic system based on parameter identification, Phys Lett A, 321, 50-55 (2004) · Zbl 1118.81326
[28] Huang, D. B., Synchronization-based estimation of all parameters of chaotic systems from time series, Phys Rev E, 69, 067201 (2004)
[29] Zhou, J.; Chen, T.; Xiang, L., Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos, Solitons & Fractals, 27, 905-913 (2006) · Zbl 1091.93032
[30] Zhou, F.; Nossek, J., Bifurcation and chaos in cellular neural networks, IEEE Trans Circuit Syst I, 40, 3, 166-173 (1993) · Zbl 0782.92003
[31] Cao, J., New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys Lett A, 307, 136-147 (2003) · Zbl 1006.68107
[32] Kuang, Y., Delay differential equations with application in population dynamics (1993), Academic Press Inc.: Academic Press Inc. New York
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