World Academy of Science, Engineering and Technology
Published July 28, 2010 | Version 2489
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PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays

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In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

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  • S. Arik, V. Tavsanoglu. Equilibrium analysis of delayed CNNs, IEEE Trans Circuits Syst. 1998, 45: 168-171.
  • S. Blythea, X. Mao, and X. Liao. Stability of stochastic delay neural networks. J. Franklin Inst, 2001, 338: 481-495.
  • J. Cao. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 2003, 307: 136-147.
  • J. Cao, J.Wang. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst, 2003, 50: 34-44.
  • J. Cao, J. Wang. Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst, 2005, 52: 417-426.
  • T. Chen,W. Lu, and G. Chen, Dynamical behaviors of a large class of general delayed neural networks, Neural Comput, 2005, 17 :949-968.
  • L.O. Chua, L.Yang. Cellular neural networks: theory. IEEE Trans. Circuits Syst, 1988, 35: 1257-1272.
  • T. Ensari, S. Arik. Global stability of a class of neural networks with time-varying delay. IEEE Trans. Circuits Syst., 2005, 52: 126-130.
  • A. Friedman. Stochastic Differential Equations and Applications. Academic Press, NewYork, 1976 [10] S. Haykin. Neural Networks. Prentice-Hall, Englewood Cliffs, NJ, 1994. [11] J. Hopfield. Neurons with graded response have collective computational properties like those of two-stage neurons. Proc. Nat. Acad. Sci. USA., 1984, 81: 3088-3092. [12] R. Horn, C. Johnson. Matrix Analysis. Cambridge University Press, London, 1985. [13] X. Liao, X. Mao. Stability of stochastic neural networks, Neural Parallel Sci. Comput., 1996, 4: 205-224. [14] X. Liao, X. Mao. Exponential stability and instability of stochastic neural networks. Stochast. Anal. Appl., 1996, 14: 165-185. [15] X. Liao, X. Mao. Exponential stability of stochastic delay interval systems. Syst. Control. Lett., 2000, 40: 171-181. [16] X. Mao. Exponential Stability of Stochastic Differential Equations. Marcel Dekker, NewYork, 1994. [17] X. Mao. Razumikihin-type theorems on exponential stability of stochastic functional differential equations. Stochast. Proc. Appl., 1996, 65: 233- 250. [18] X. Mao. Robustness of exponential stability of stochastic differential delay equations. IEEE Trans. Automat. Control., 1996, 41 :442-447. [19] X. Mao. Stochastic Differential Equations and Applications. Horwood Publication, Chichester, 1997. [20] S. Mohammed. Stochastic Functional Differential Equations. Longman Scientific and Technical, 1986. [21] S. Mohamad, K. Gopalsamy. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl. Math. Comput., 2003, 135: 17-38. [22] L.Wan, J. Sun. Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A., 2005, 343: 306-318. [23] H. Zhao. Global exponential stability and periodicity of cellular neural networks with variable delays. Phys. Lett. A., 2005, 336: 331-341. [24] J. Zhang. Globally exponential stability of neural networks with variable delays. IEEE Trans. Circuits Syst., 2003, 50: 288-291. [25] Z. Zeng, J. Wang, and X. Liao. Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst., 2003, 50: 1353-1358. [26] J. Cao, Q. Song. Stability in Cohen-Grossberg type BAM neural networks with time-varying delays. Nonlinearity, 2006, 19: 1601-1617. [27] J. Cao, J. Lu. Adaptive synchronization of neural networks with or without time-varying delays. Chaos, 2006, 16: 013133. [28] J. Cao et al., Global point dissipativity of neural networks with mixed time-varying delays. Chaos, 2006, 16: 013105. [29] Y. Sun,J. Cao. pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. Nonlinear Analysis: RealWorld Applications, 2007, 8: 1171-1185.