{"title":"PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays","authors":"Zixin Liu, Jianjun Jiao Wanping Bai","volume":43,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":788,"pagesEnd":795,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2489","abstract":"
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.<\/p>\r\n","references":"[1] S. Arik, V. Tavsanoglu. Equilibrium analysis of delayed CNNs, IEEE\r\nTrans Circuits Syst. 1998, 45: 168-171.\r\n[2] S. Blythea, X. Mao, and X. Liao. Stability of stochastic delay neural\r\nnetworks. J. Franklin Inst, 2001, 338: 481-495.\r\n[3] J. Cao. New results concerning exponential stability and periodic solutions\r\nof delayed cellular neural networks. Phys. Lett. A 2003, 307:\r\n136-147.\r\n[4] J. Cao, J.Wang. Global asymptotic stability of a general class of recurrent\r\nneural networks with time-varying delays. IEEE Trans. Circuits Syst,\r\n2003, 50: 34-44.\r\n[5] J. Cao, J. Wang. Global asymptotic and robust stability of recurrent neural\r\nnetworks with time delays, IEEE Trans. Circuits Syst, 2005, 52: 417-426.\r\n[6] T. Chen,W. Lu, and G. Chen, Dynamical behaviors of a large class of\r\ngeneral delayed neural networks, Neural Comput, 2005, 17 :949-968.\r\n[7] L.O. Chua, L.Yang. Cellular neural networks: theory. IEEE Trans.\r\nCircuits Syst, 1988, 35: 1257-1272.\r\n[8] T. Ensari, S. Arik. Global stability of a class of neural networks with\r\ntime-varying delay. IEEE Trans. Circuits Syst., 2005, 52: 126-130.\r\n[9] A. Friedman. Stochastic Differential Equations and Applications. Academic\r\nPress, NewYork, 1976\r\n[10] S. Haykin. Neural Networks. Prentice-Hall, Englewood Cliffs, NJ, 1994.\r\n[11] J. Hopfield. Neurons with graded response have collective computational\r\nproperties like those of two-stage neurons. Proc. Nat. Acad. Sci. USA.,\r\n1984, 81: 3088-3092.\r\n[12] R. Horn, C. Johnson. Matrix Analysis. Cambridge University Press,\r\nLondon, 1985.\r\n[13] X. Liao, X. Mao. Stability of stochastic neural networks, Neural Parallel\r\nSci. Comput., 1996, 4: 205-224.\r\n[14] X. Liao, X. Mao. Exponential stability and instability of stochastic\r\nneural networks. Stochast. Anal. Appl., 1996, 14: 165-185.\r\n[15] X. Liao, X. Mao. Exponential stability of stochastic delay interval\r\nsystems. Syst. Control. Lett., 2000, 40: 171-181.\r\n[16] X. Mao. Exponential Stability of Stochastic Differential Equations.\r\nMarcel Dekker, NewYork, 1994.\r\n[17] X. Mao. Razumikihin-type theorems on exponential stability of stochastic\r\nfunctional differential equations. Stochast. Proc. Appl., 1996, 65: 233-\r\n250.\r\n[18] X. Mao. Robustness of exponential stability of stochastic differential\r\ndelay equations. IEEE Trans. Automat. Control., 1996, 41 :442-447.\r\n[19] X. Mao. Stochastic Differential Equations and Applications. Horwood\r\nPublication, Chichester, 1997.\r\n[20] S. Mohammed. Stochastic Functional Differential Equations. Longman\r\nScientific and Technical, 1986.\r\n[21] S. Mohamad, K. Gopalsamy. Exponential stability of continuous-time\r\nand discrete-time cellular neural networks with delays. Appl. Math.\r\nComput., 2003, 135: 17-38.\r\n[22] L.Wan, J. Sun. Mean square exponential stability of stochastic delayed\r\nHopfield neural networks. Phys. Lett. A., 2005, 343: 306-318.\r\n[23] H. Zhao. Global exponential stability and periodicity of cellular neural\r\nnetworks with variable delays. Phys. Lett. A., 2005, 336: 331-341.\r\n[24] J. Zhang. Globally exponential stability of neural networks with variable\r\ndelays. IEEE Trans. Circuits Syst., 2003, 50: 288-291.\r\n[25] Z. Zeng, J. Wang, and X. Liao. Global exponential stability of a general\r\nclass of recurrent neural networks with time-varying delays. IEEE Trans.\r\nCircuits Syst., 2003, 50: 1353-1358.\r\n[26] J. Cao, Q. Song. Stability in Cohen-Grossberg type BAM neural networks\r\nwith time-varying delays. Nonlinearity, 2006, 19: 1601-1617.\r\n[27] J. Cao, J. Lu. Adaptive synchronization of neural networks with or\r\nwithout time-varying delays. Chaos, 2006, 16: 013133.\r\n[28] J. Cao et al., Global point dissipativity of neural networks with mixed\r\ntime-varying delays. Chaos, 2006, 16: 013105.\r\n[29] Y. Sun,J. Cao. pth moment exponential stability of stochastic recurrent\r\nneural networks with time-varying delays. Nonlinear Analysis: RealWorld\r\nApplications, 2007, 8: 1171-1185.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 43, 2010"}