Exponential synchronization of coupled fuzzy neural networks with disturbances and mixed time-delays

This paper focuses on the exponential synchronization problem of coupled fuzzy neural networks with disturbances and mixed time-delays. For the network under study, the effects of both random and vague factors are considered. By stochastic analysis techniques, we establish sufficient conditions for the coupled fuzzy neural networks to be exponentially synchronized in the mean square. It is demonstrated that the network synchronizability is largely dependent on the coupling structure of such network. Moreover, the information exchange network needs not to be undirected or strongly connected. Finally, numerical simulations are given to verify the usefulness and effectiveness of our results.

[1]  Zhidong Teng,et al.  Exponential Synchronization of Complex Networks With Finite Distributed Delays Coupling , 2011, IEEE Transactions on Neural Networks.

[2]  Zhidong Teng,et al.  Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays , 2008, Neurocomputing.

[3]  Daniel W. C. Ho,et al.  Pinning Stabilization of Linearly Coupled Stochastic Neural Networks via Minimum Number of Controllers , 2009, IEEE Transactions on Neural Networks.

[4]  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).

[5]  Eam Khwang Teoh,et al.  Pattern recognition by homomorphic graph matching using Hopfield neural networks , 1995, Image Vis. Comput..

[6]  Song Zhu,et al.  Passivity analysis of stochastic delayed neural networks with Markovian switching , 2011, Neurocomputing.

[7]  Ling Guan,et al.  A neural network adaptive filter for the removal of impulse noise in digital images , 1996, Neural Networks.

[8]  K. Gu An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[9]  Bor-Sen Chen,et al.  Robust $H_{\infty}$ Synchronization Design of Nonlinear Coupled Network via Fuzzy Interpolation Method , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  L.O. Chua,et al.  Cellular neural networks , 1993, 1988., IEEE International Symposium on Circuits and Systems.

[11]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[12]  Jun Wang,et al.  Noise-Induced Stabilization of the Recurrent Neural Networks With Mixed Time-Varying Delays and Markovian-Switching Parameters , 2007, IEEE Transactions on Neural Networks.

[13]  Xiaodi Li,et al.  Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks , 2012, Fuzzy Sets Syst..

[14]  Yang Tang,et al.  Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling , 2009, Neurocomputing.

[15]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[16]  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.

[17]  Yi Shen,et al.  The almost sure asymptotic stability and pth moment asymptotic stability of nonlinear stochastic delay differential systems with polynomial growth , 2012 .

[18]  Zijiang Yang,et al.  Lag Synchronization of Unknown Chaotic Delayed Yang–Yang-Type Fuzzy Neural Networks With Noise Perturbation Based on Adaptive Control and Parameter Identification , 2009, IEEE Transactions on Neural Networks.

[19]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[20]  Xiaofan Wang,et al.  On synchronization in scale-free dynamical networks , 2005 .

[21]  Jun Wang,et al.  Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching , 2009, IEEE Transactions on Neural Networks.

[22]  Zhigang Zeng,et al.  Associative memories based on continuous-time cellular neural networks designed using space-invariant cloning templates , 2009, Neural Networks.

[23]  Liping Chen,et al.  Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays , 2011, Expert Syst. Appl..

[24]  W. Stewart,et al.  The Kronecker product and stochastic automata networks , 2004 .

[25]  Zhidong Teng,et al.  Boundedness and stability for nonautonomous bidirectional associative neural networks with delay , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[26]  Zhigang Zeng,et al.  Synchronization control of a class of memristor-based recurrent neural networks , 2012, Inf. Sci..

[27]  Haijun Jiang,et al.  Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms , 2011, Neurocomputing.

[28]  Chin-Teng Lin,et al.  A Recurrent Fuzzy Coupled Cellular Neural Network System With Automatic Structure and Template Learning , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[30]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[31]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[32]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[34]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  C. Wu Synchronization in networks of nonlinear dynamical systems coupled via a directed graph , 2005 .

[36]  Zhidong Teng,et al.  Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control , 2012, Math. Comput. Simul..

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

[38]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[39]  Chen An,et al.  The Global Stability of Fuzzy Cellular Neural Networks , 2001 .