Synchronization control for arrays of coupled discrete-time delayed Cohen-Grossberg neural networks

This paper investigates the global exponential synchronization for an array of coupled discrete-time Cohen-Grossberg neural networks (CGNNs) with time-varying delay, in which both the constant coupling and delayed one are considered. Through constructing an improved Lyapunov-Krasovskii functional, the delay-dependent sufficient condition is obtained to guarantee the global synchronization based on linear matrix inequality (LMI) approach. The criterion is presented in terms of LMIs and its feasibility can be easily checked by resorting to Matlab LMI Toolbox. Moreover, the addressed system can include some famous neural network models as its special cases, which can help extend those present results. Finally, the effectiveness of the proposed method can be further illustrated with the help of two numerical examples.

[1]  Zidong Wang,et al.  Global Synchronization Control of General Delayed Discrete-Time Networks With Stochastic Coupling and Disturbances , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Aiguo Song,et al.  Novel Stability Criteria on Discrete-Time Neural Networks with Both Time-Varying and Distributed Delays , 2009, Int. J. Neural Syst..

[3]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[4]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  L. Chua,et al.  COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS , 1994 .

[6]  Xuyang Lou,et al.  Synchronization of neural networks based on parameter identification and via output or state coupling , 2008 .

[7]  Swarup Poria,et al.  Synchronization of bidirectionally coupled chaotic Chen's system with delay , 2009 .

[8]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[9]  J Kurths,et al.  Stability of synchronization in coupled time-delay systems using Krasovskii-Lyapunov theory. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Jitao Sun,et al.  Robust synchronization of coupled delayed neural networks under general impulsive control , 2009 .

[11]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

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

[13]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

[14]  Jun-an Lu,et al.  Impulsive synchronization of general continuous and discrete-time complex dynamical networks , 2010 .

[15]  Xiefu Jiang,et al.  Stability criteria for linear discrete-time systems with interval-like time-varying delay , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Elbert E. N. Macau,et al.  Detecting phase synchronization between coupled non-phase-coherent oscillators , 2009 .

[18]  Maoan Han,et al.  Synchronization schemes for coupled identical Yang–Yang type fuzzy cellular neural networks , 2009 .

[19]  Hamid Reza Karimi,et al.  Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks , 2009 .

[20]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[21]  Pawel Bujnowski,et al.  Aspiration and Cooperation in Multiperson Prisoner's Dilemma , 2009 .

[22]  A. G. Naim,et al.  Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks , 2002 .

[23]  L. Chua,et al.  Application of graph theory to the synchronization in an array of coupled nonlinear oscillators , 1995 .

[24]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[25]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[26]  Xiaohua Ding,et al.  Synchronization in time-discrete delayed chaotic systems , 2009, Neurocomputing.

[27]  Kun Yuan,et al.  Robust synchronization in arrays of coupled networks with delay and mixed coupling , 2009, Neurocomputing.

[28]  Wei Xing Zheng,et al.  New Synchronization Stability of Complex Networks With an Interval Time-Varying Coupling Delay , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Wei Wu,et al.  Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling , 2008, IEEE Transactions on Neural Networks.

[30]  Zhi Li,et al.  New approach to synchronization in asymmetrically coupled networks , 2008 .

[31]  Jinde Cao,et al.  Global synchronization in arrays of coupled networks with one single time-varying delay coupling , 2009 .

[33]  Leon O. Chua,et al.  Spiral waves on a 2-D array of nonlinear circuits , 1993 .

[34]  Jian-An Fang,et al.  Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays , 2010 .

[35]  Jinde Cao,et al.  Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[36]  Tianping Chen,et al.  Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix , 2008 .

[37]  Qiankun Song,et al.  Synchronization analysis of coupled connected neural networks with mixed time delays , 2009, Neurocomputing.

[38]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .

[39]  Zidong Wang,et al.  Exponential synchronization of stochastic delayed discrete-time complex networks , 2008 .

[40]  Sezai Emre Tuna,et al.  Conditions for Synchronizability in Arrays of Coupled Linear Systems , 2008, IEEE Transactions on Automatic Control.