Stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities

This paper focuses on stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities and random coupling strengths. The coupling configuration matrices are not restricted to be symmetric, and the coupling strengths are mutually independent random variables. By designing a novel augmented Lyapunov-Krasovskii functional and using reciprocally convex combination technique and the properties of random variables, new delay-dependent synchronization criteria in terms of linear matrix inequalities are derived. The obtained criteria depend not only on upper and lower bounds of delay but also on mathematical expectations and variances of random coupling strengths. Numerical examples are provided to verify the effectiveness of the presented results.

[1]  Zidong Wang,et al.  Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays , 2013, IEEE Transactions on Cybernetics.

[2]  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).

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

[4]  Dong Yue,et al.  Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays , 2010, Neurocomputing.

[5]  Qian Ma,et al.  Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities , 2011, Neurocomputing.

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

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

[8]  Wenwu Yu,et al.  Distributed Adaptive Control of Synchronization in Complex Networks , 2012, IEEE Transactions on Automatic Control.

[9]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

[10]  Jie Chen,et al.  Introduction to Time-Delay Systems , 2003 .

[11]  Wai Keung Wong,et al.  Distributed Synchronization of Coupled Neural Networks via Randomly Occurring Control , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[13]  Peng Shi,et al.  Sampled-Data Exponential Synchronization of Complex Dynamical Networks With Time-Varying Coupling Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[15]  Ya Zhang,et al.  Global synchronization of stochastic delayed complex networks , 2012, Nonlinear Dynamics.

[16]  Jinde Cao,et al.  Local Synchronization of a Complex Network Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Jie Zhang,et al.  Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices , 2011, Autom..

[18]  Jinde Cao,et al.  Synchronization of Markovian Coupled Neural Networks With Nonidentical Node-Delays and Random Coupling Strengths , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Huaguang Zhang,et al.  Local exponential synchronization in complex dynamical networks with time-varying delay and hybrid coupling , 2013, Appl. Math. Comput..

[20]  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.

[21]  Shengyuan Xu,et al.  Global Exponential Adaptive Synchronization of Complex Dynamical Networks With Neutral-Type Neural Network Nodes and Stochastic Disturbances , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[23]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[24]  Huaguang Zhang,et al.  Synchronization stability in complex interconnected neural networks with nonsymmetric coupling , 2013, Neurocomputing.

[25]  Jinde Cao,et al.  Cluster synchronization in an array of hybrid coupled neural networks with delay , 2009, Neural Networks.

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

[27]  Huaguang Zhang,et al.  Novel synchronization analysis for complex networks with hybrid coupling by handling multitude Kronecker product terms , 2012, Neurocomputing.

[28]  Bing Chen,et al.  Synchronization for Coupled Neural Networks With Interval Delay: A Novel Augmented Lyapunov–Krasovskii Functional Method , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  Jun Zhao,et al.  Global Bounded Synchronization of General Dynamical Networks With Nonidentical Nodes , 2012, IEEE Transactions on Automatic Control.