Pinning Synchronization Control of Stochastic Neural Networks with Time Delays

In this paper, the asymptotic stability of the pinning synchronous solution of stochastic neural networks with time delays is analyzed. The delays are time-invariant, and the uncertainties are norm bounded that enter into all the parameters of network and control. The aim of this paper is not only to establish easily verifiable conditions under which the pinning synchronous solution of stochastic neural network is globally asymptotically stable, but also to give a feasible way to offset the limitation of network itself in order to reach synchronization. In addition, a specific neurobiological network is also introduced and some numerical examples are provided to illustrate the applicability of the proposed criteria.

[1]  F. Garofalo,et al.  Pinning-controllability of complex networks , 2007, cond-mat/0701073.

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

[3]  L. Arnold Stochastic Differential Equations: Theory and Applications , 1992 .

[4]  Kristin Y. Pettersen,et al.  Output synchronization control of ship replenishment operations: Theory and experiments , 2007 .

[5]  Leon O. Chua,et al.  Stability and dynamics of delay-type general and cellular neural networks , 1992 .

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

[7]  M. Small,et al.  Pinning synchronization of delayed neural networks. , 2008, Chaos.

[8]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[9]  J. Casado,et al.  Noise-induced resonances in the Hindmarsh-Rose neuronal model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Bin Deng,et al.  Robust synchronization control of coupled chaotic neurons under external electrical stimulation , 2009 .

[11]  Hsin-Chieh Chen,et al.  EP-based PID control design for chaotic synchronization with application in secure communication , 2008, Expert Syst. Appl..

[12]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Shihua Chen,et al.  Pinning synchronization of the complex networks with non-delayed and delayed coupling , 2009 .

[14]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[15]  Her-Terng Yau,et al.  Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control , 2008 .

[16]  Lu Qi-Shao,et al.  Coherence resonance and synchronization of Hindmarsh Rose neurons with noise , 2005 .

[17]  Lu Qi-Shao,et al.  Complete Synchronization of Coupled Hindmarsh–Rose Neurons with Ring Structure , 2004 .

[18]  H Sabbagh,et al.  Control of chaotic solutions of the Hindmarsh–Rose equations , 2000 .

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