Exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, we deal with the exponential synchronization problem for a class of stochastic perturbed chaotic delayed neural networks. Based on the Lyapunov stability theory, by virtue of stochastic analysis, Halanay inequality for stochastic differential equations, drive-response concept and time-delay feedback control techniques, several sufficient conditions are proposed to guarantee the exponential synchronization of two identical chaotic delayed neural networks with stochastic perturbation. These conditions, which are expressed in terms of linear matrix inequalities, rely on the connection matrix in the drive networks as well as the suitable designed feedback gains in the response networks. Finally, a numerical example with its simulations are provided to illustrate the effectiveness of the presented synchronization scheme.

[1]  K. Gopalsamy,et al.  Continuous and discrete Halanay-type inequalities , 2000, Bulletin of the Australian Mathematical Society.

[2]  Guo-Ping Jiang,et al.  A New Criterion for Chaos Synchronization Using Linear State Feedback Control , 2003, Int. J. Bifurc. Chaos.

[3]  Jinde Cao.  New results concerning exponential stability and periodic solutions of delayed cellular neural networks , 2003 .

[4]  X. Mao,et al.  Exponential Stability of Stochastic Di erential Equations , 1994 .

[5]  T. Liao,et al.  Synchronization of neural networks by decentralized feedback control , 2005 .

[6]  Jinde Cao,et al.  Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. , 2005, Chaos.

[7]  Guanrong Chen,et al.  Chaos Synchronization of General Lur'e Systems via Time-Delay Feedback Control , 2003, Int. J. Bifurc. Chaos.

[8]  Jinde Cao.  Periodic oscillation and exponential stability of delayed CNNs , 2000 .

[9]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[10]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[11]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[12]  Jinde Cao,et al.  Synchronization criteria of Lur’e systems with time-delay feedback control , 2005 .

[13]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[14]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[15]  M. Gilli.  Strange attractors in delayed cellular neural networks , 1993 .

[16]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[17]  Guanrong Chen,et al.  Chaos synchronization of general complex dynamical networks , 2004 .

[18]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of neural networks with time-varying delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Xiaofan Wang,et al.  Generating chaos in Chua's circuit via time-delay feedback , 2001 .

[20]  A. Friedman.  Stochastic Differential Equations and Applications , 1975 .

[21]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[22]  Vicente Pérez-Muñuzuri,et al.  ANALYSIS OF SYNCHRONIZATION OF CHAOTIC SYSTEMS BY NOISE: AN EXPERIMENTAL STUDY , 1997 .

[23]  Zhang Yifeng,et al.  A secure communication scheme based on cellular neural network , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[24]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of chaotic neural networks , 2005 .

[26]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[27]  Xuerong Mao,et al.  Exponential stability and instability of stochastic neural networks 1 , 1996 .

[28]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[29]  Gang Hu,et al.  Synchronization of a one-dimensional array of Chua's circuits by feedback control and noise , 1995 .

[30]  Daniel W. C. Ho,et al.  Synchronization Criteria for Lur'e Systems by Dynamic Output Feedback with Time-Delay , 2006, Int. J. Bifurc. Chaos.

[31]  K. Wong,et al.  Noise and synchronization in chaotic neural networks , 1998 .

[32]  Maosheng Wang,et al.  Internal noise-enhanced phase synchronization of coupled chemical chaotic oscillators , 2005 .

[33]  Wei Lin,et al.  Complete synchronization of the noise-perturbed Chua's circuits. , 2005, Chaos.

[34]  Jinde Cao,et al.  Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme , 2006 .

[35]  Evelyn Buckwar,et al.  Exponential stability in p -th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations , 2005 .

[36]  Jin Xu,et al.  On the global stability of delayed neural networks , 2003, IEEE Trans. Autom. Control..

[37]  Jianhua Sun,et al.  Mean square exponential stability of stochastic delayed Hopfield neural networks , 2005 .