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.


93D15 Stabilization of systems by feedback
37N35 Dynamical systems in control
34K20 Stability theory of functional-differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34H10 Chaos control for problems involving ordinary differential equations
93C23 Control/observation systems 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
[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
[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
[6] Gilli, M., Strange attractors in delayed cellular neural networks, IEEE trans circuits syst I, 40, 849-853, (1993) · Zbl 0844.58056
[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) · Zbl 1371.92015
[8] Karimi, H.R.; Gao, H., New delay-dependent exponential H∞ 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
[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
[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
[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
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.