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Synchronization of chaotic neural networks with mixed time delays. (English) Zbl 1221.93222
Summary: We investigate the synchronization problems of chaotic neural networks with mixed time delays. We first establish the sufficient conditions for synchronization of identical chaotic neural networks with mixed time delays via linear output feedback control. To overcome the difficulty that complete synchronization between nonidentical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of nonidentical chaotic neural networks with mixed time delays, where the parameters and functions are mismatched. Numerical simulations are carried out to illustrate the main results.

93D15Stabilization of systems by feedback
37N35Dynamical systems in control
34K20Stability theory of functional-differential equations
37D45Strange attractors, chaotic dynamics
34H10Chaos control (ODE)
93C23Systems governed by functional-differential equations
Full Text: DOI
[1] Astakhov, V.; Hasler, M.; Kapitaniak, T.; Shabunin, A.; Anishchenko, V.: Effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems, Phys rev E 58, 5620-5628 (1998)
[2] Ayrulu, B.; Barshan, B.: Neural networks for improved target differentiation and localization with sonar, Neural networks 14, 355-373 (2001)
[3] Blythe, S.; Mao, X.; Liao, X.: Stability of stochastic delay neural networks, J franklin inst 338, 481-495 (2001) · Zbl 0991.93120 · doi:10.1016/S0016-0032(01)00016-3
[4] Cannas, B.; Cincotti, S.; Marchesi, M.; Pilo, F.: Learning of Chua’s circuit attractors by locally recurrent neural networks, Chaos, solitons fractals 12, 2109-2115 (2001) · Zbl 0981.68135 · doi:10.1016/S0960-0779(00)00174-0
[5] Chen, M.; Chen, W.: Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems, Chaos, solitons fractals 41, 2716-2724 (2002) · Zbl 1198.93155 · doi:10.1016/j.chaos.2008.10.003
[6] Gilli, M.: Strange attractors in delayed cellular neural networks, IEEE trans circuits syst I 40, 849-853 (1993) · Zbl 0844.58056 · doi:10.1109/81.251826
[7] Hopfield, J.: Neurons with graded response have collective computational properties like those of two-state neurons, Proc nat acad sci USA 81, 3088-3092 (1984)
[8] Karimi, H. R.; Gao, H.: New delay-dependent exponential H$\infty $ synchronization for uncertain neural networks with mixed time delays, IEEE trans syst, man, cybern B, cybern 40, 173-185 (2010)
[9] Leung, H.; Zhu, Z.: Time-varying synchronization of chaotic systems in the presence of system mismatch, Phys rev E 69, 026201 (2004)
[10] Li, T.; Fei, S.; Zhu, Q.; Cong, S.: Exponential synchronization of chaotic neural networks with mixed delays, Neurocomputing 71, 3005-3019 (2008)
[11] Li, T.; Song, A.; Fei, S.; Guo, Y.: Synchronization control of chaotic neural networks with time-varying and distributed delays, Nonlinear anal 71, 2372-2384 (2008) · Zbl 1171.34049 · doi:10.1016/j.na.2009.01.079
[12] Liu, B.; Huang, L.: Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Chaos, solitons fractals 31, 211-217 (2007) · Zbl 1161.34352 · doi:10.1016/j.chaos.2005.09.052
[13] Lu, J.; Chen, G.: Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: an LMI approach, Chaos, solitons fractals 41, 2293-2300 (2009) · Zbl 1198.37141 · doi:10.1016/j.chaos.2008.09.024
[14] Otawara, K.; Fan, L.; Tsutsumi, A.; Yano, T.; Kuramoto, K.; Yoshida, K.: An artificial neural network as a model for chaotic behavior of a three-phase fluidized bed, Chaos, solitons fractals 13, 353-362 (2002) · Zbl 1073.76656 · doi:10.1016/S0960-0779(00)00250-2
[15] Quek, C.; Tan, K. B.; Sagar, V. K.: Pseudo-outer product based fuzzy neural networks fingerprint verification system, Neural networks 14, 305-323 (2001)
[16] Ramesh, M.; Narayanan, S.: Chaos control of bonhoeffer-van der Pol oscillator using neural networks, Chaos, solitons fractals 12, 2395-2405 (2001) · Zbl 1004.37067 · doi:10.1016/S0960-0779(00)00200-9
[17] Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach, IEEE proc control theory appl 151, 125-129 (2004)
[18] Song, Q.: Design of controller on synchronization of chaotic neural networks with mixed time-varying delays, Neurocomputing 72, 3288-3295 (2009)
[19] Song, Q.: Synchronization analysis of coupled connected neural networks with mixed time delays, Neurocomputing 72, 3907-3914 (2009)
[20] Wu, C.; Chua, L. O.: A unified framework for synchronization and control of dynamical systems, Int J bifurcation chaos 4, 979-989 (1994) · Zbl 0875.93445 · doi:10.1142/S0218127494000691