Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays. (English) Zbl 1221.93247

Summary: This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.


93D21 Adaptive or robust stabilization
34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92B20 Neural networks for/in biological studies, artificial life and related topics
Full Text: DOI


[1] Agiza, H. N.; Yassen, M. T., Synchronization of Rossler and Chen chaotic dynamical systems using active control, Phys Lett A, 278, 4, 191-197 (2001) · Zbl 0972.37019
[2] Boyd, S.; Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[3] Carroll, T. L.; Pecora, L. M., Synchronization chaotic circuits, IEEE Trans Circuit Syst, 38, 4, 453-456 (1991)
[4] Cao, J.; Lu, J., Adaptive synchronization of neural networks with or without time-varying delays, Chaos, 16, 1, 013133 (2006) · Zbl 1144.37331
[5] Cui, B.; Lou, X., Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control, Chaos Soliton Fract, 39, 1, 288-294 (2009) · Zbl 1197.93135
[6] Fotsin, H. B.; Woafo, P., Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification, Chaos Soliton Fract, 24, 5, 1363-1371 (2005) · Zbl 1091.70010
[7] Fotsin, H. B.; Daafouz, J., Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification, Phys Lett A, 339, 3-5, 304-315 (2005) · Zbl 1145.93313
[10] He, G.; Cao, Z.; Zhu, P.; Ogura, H., Controlling chaos in a chaotic neural network, Neural Networks, 16, 8, 1195-1200 (2003)
[11] Heagy, J. F.; Carroll, T. L.; Pecora, L. M., Experimental and numerical evidence for riddled basins in coupled chaotic systems, Phys Rev Lett, 73, 26, 3528-3531 (1994)
[12] Huang, D., Simple adaptive-feedback controller for identical chaos synchronization, Phys Rev E, 71, 037203 (2005)
[13] Huang, L.; Feng, R.; Wang, M., Synchronization of chaotic systems via nonlinear control, Phys Lett A, 320, 4, 271-275 (2004) · Zbl 1065.93028
[14] Kakmeni, F.; Bowong, S.; Tchawoua, C., Nonlinear adaptive synchronization of a class of chaotic systems, Phys Lett A, 355, 1, 47-54 (2006) · Zbl 1130.93404
[15] Li, X.; Cao, J., Adaptive synchronization for delayed neural networks with stochastic perturbation, J Franklin Inst, 345, 7, 779-791 (2008) · Zbl 1169.93350
[16] Li, C.; Liao, X.; Yang, X.; Huang, T., Impulsive stabilization and synchronization of a class of chaotic delay systems, Chaos, 15, 023104 (2005) · Zbl 1080.37034
[17] Li, T.; Fei, S.; Zhu, Q.; Cong, S., Exponential synchronization of chaotic neural networks with mixed delays, Neurocomputing, 71, 13-15, 3005-3019 (2008)
[18] Lei, Y.; Xu, W.; Zheng, H., Synchronization of two chaotic nonlinear gyros using active control, Phys Lett A, 343, 1-3, 153-158 (2005) · Zbl 1194.34090
[19] 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
[20] Mahboobi, S. H.; Shahrokhi, M.; Pishkenari, H. N., Observer-based control design for three well-known chaotic systems, Chaos Soliton Fract, 29, 2, 381-392 (2006) · Zbl 1147.93390
[21] Mao, X., Stochastic differential equation and application (1997), Horwood Publishing: Horwood Publishing Chichester · Zbl 0874.60050
[22] Mao, X., A note on the LaSalle-type theorems for stochastic differential delay equations, J Math Anal Appl, 268, 1, 125-142 (2002) · Zbl 0996.60064
[23] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys Rev Lett, 64, 8, 821-824 (1990) · Zbl 0938.37019
[24] Park, J. H., Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters, J Comput Appl Math, 213, 1, 288-293 (2008) · Zbl 1137.93035
[25] Park, J. H., Synchronization of Genesio chaotic system via backstepping approach, Chaos Soliton Fract, 27, 5, 1369-1375 (2006) · Zbl 1091.93028
[26] Salarieh, H.; Alasty, A., Adaptive synchronization of two chaotic systems with stochastic unknown parameters, Commun Nonlinear Sci Numer Simulat, 14, 2, 508-519 (2009) · Zbl 1221.93246
[27] Sun, Y.; Cao, J.; Wang, Z., Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing, 70, 13-15, 2477-2485 (2007)
[28] Tang, Y.; Qiu, R.; Fang, J.; Miao, Q.; Xia, M., Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays, Phys Lett A, 372, 24, 4425-4433 (2008) · Zbl 1221.82078
[29] Wang, C.; Su, J., A new adaptive variable structure control for chaotic synchronization and secure communication, Chaos Soliton Fract, 20, 5, 967-977 (2004) · Zbl 1050.93036
[30] Wang, K.; Teng, Z.; Jiang, H., Adaptive synchronization of neural networks with time-varying delay and distributed delay, Physica A, 387, 2-3, 631-642 (2008)
[31] Yang, Y.; Cao, J., Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects, Physica A, 386, 1, 492-502 (2007)
[32] Yu, W.; Cao, J., Synchronization control of stochastic delayed neural networks, Physica A, 373, 1, 252-260 (2007)
[33] Zhou, J.; Chen, T.; Xiang, L., Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos Soliton Fract, 27, 4, 905-913 (2006) · Zbl 1091.93032
[34] Zhu, Q.; Cao, J., Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays, Nonlinear Dyn, 61, 3, 517-534 (2010) · Zbl 1204.93064
[35] Zhu, Q.; Cao, J., Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays, Discrete Dyn Nat Soc, 2009, 20 (2009), Article ID 490515 · Zbl 1185.93147
[36] Zhu, Q.; Cao, J., Robust exponential stability of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans Neural Networks, 21, 8, 1314-1325 (2010)
[38] Zhu, Q.; Cao, J., Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays, Neurocomputing, 73, 13-15, 2671-2680 (2010)
[39] Zhu, Q.; Yang, X.; Wang, H., Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances, J Franklin Inst, 347, 2, 1489-1510 (2010) · Zbl 1202.93169
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