Adaptive synchronization for delayed neural networks with stochastic perturbation. (English) Zbl 1169.93350

Summary: In this paper, an adaptive feedback controller is designed to achieve complete synchronization of unidirectionally coupled delayed neural networks with stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example and numerical simulation are given to demonstrate the effectiveness of the theory results.


93C40 Adaptive control/observation systems
93B52 Feedback control
93C73 Perturbations in control/observation systems
93E03 Stochastic systems in control theory (general)
Full Text: DOI


[1] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[2] Pecora, L. M.; Carroll, T. L.; Johnson, G. A., Fundamentals of synchronization in chaotic systems, concepts, and applications, Chaos, 7, 520-543 (1998) · Zbl 0933.37030
[3] Ott, E.; Grebogi, C.; Yorke, J., Controlling chaos, Phys. Rev. Lett., 64, 1196-1199 (1990) · Zbl 0964.37501
[4] Heagy, J. F.; Carroll, T. L.; Pecora, L. M., Experimental and numerical evidence for riddled basins in coupled chaotic systems, Phys. Rev. Lett., 73, 3528-3531 (1994)
[5] Yang, X.; Duan, C.; Liao, X., A note on mathematical aspects of drive-response type synchronization, Chaos Solitons Fractals, 10, 1457-1462 (1999) · Zbl 0955.37020
[6] Huang, D., Simple adaptive-feedback controller for identical chaos synchronization, Phys. Rev. E, 71, 037203 (2005)
[7] Lu, J.; Cao, J., Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters, Chaos, 15, 043901 (2005) · Zbl 1144.37378
[8] Cao, J.; Li, H.; Ho, D., Synchronization criteria of Lur’e systems with time-delay feedback control, Chaos Solitons Fractals, 23, 1285-1293 (2005) · Zbl 1086.93050
[9] Li, C.; Liao, X.; Zhang, X., Impulsive stabilization and synchronization of a class of chaotic delay systems, Chaos, 15, 023104 (2005) · Zbl 1080.37034
[10] Gilli, M., Strange attactors in delayed cellular neural networks, IEEE Trans. Circuits Syst. I, 40, 849-853 (1993) · Zbl 0844.58056
[11] Lu, H., Chaotic attractors in delayed neural networks, Phys. Lett. A, 298, 109-116 (2002) · Zbl 0995.92004
[12] Chen, G.; Zhou, J.; Liu, Z., Global synchronizaton of coupled delayed neural networks and applications to chaotic CNN model, Int. J. Bifurcation Chaos, 14, 2229-2240 (2004) · Zbl 1077.37506
[13] Zhang, Y.; He, Z., A secure communication scheme based on cellular neural networks, IEEE Int. Conf. Intell. Process. Syst., 1, 521-524 (1997)
[14] 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
[15] Cheng, C.; Liao, T.; Hwang, C., Exponential synchronization of a class of chaotic neural networks, Chaos Solitons Fractals, 24, 197-206 (2005) · Zbl 1060.93519
[16] Haykin, S., Neural Networks (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0828.68103
[17] Lin, W.; He, Y., Complete synchronization of the noise-perturbed Chua’s circuits, Chaos, 15, 023705 (2005)
[18] Pakdamana, K.; Mestivier, D., Noise induced synchronization in a neuronal oscillator, Physica D, 192, 123-137 (2004) · Zbl 1055.92013
[19] Huang, D., Stabilizing near-nonhyperbolic chaos systems with applications, Phys. Rev. Lett., 93, 214101 (2004)
[20] Cao, J.; Lu, J., Adaptive synchronization of neural networks with or without time-varying delays, Chaos, 16, 013133 (2006) · Zbl 1144.37331
[22] Mao, X., Exponential Stability of Stochastic Differential Equations (1994), Marcel Dekker: Marcel Dekker New York · Zbl 0851.93074
[23] Mao, X., A note on the LaSalle-type theorems for stochastic differential delay equations, J. Math. Anal. Appl., 268, 125-142 (2002) · Zbl 0996.60064
[24] Higham, D., An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Review, 43, 525-546 (2001) · Zbl 0979.65007
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.