pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.

Keywords: pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079284

References:

[1] T .L. Carroll, L .M. Pecora. Synchronization in chaotic systems. Phys. Rev. Lett, 1990, 64: 821-824.
[2] T .L. Carroll, L .M. Pecora. Synchronizing chaotic circuits. IEEE Trans. Circ. Syst, 1991, 38: 453-456.
[3] T .Li, S .M. Fei, K .J. Zhang. Synchronization control of recurrent neural networks with distributed delays. Physica A, 2008, 387: 982-996.
[4] T .Liu, G .M. Dimirovskib, J .Zhao. Exponential synchronization of complex delayed dynamical networks with general topology. Phys. Lett. A, 2008, 387: 643-652.
[5] X .Lou, B .Cui. Synchronization of neural networks based on parameter identification and via output or state coupling, Journal of Computational and Applied Mathematics (2007), doi:10.1016/j.cam.2007.11.015.
[6] S .Li. et al., Adaptive exponential synchronization of delayed ..., Chaos, Solitons, Fractals (2007), doi:10.1016/j.chaos.2007.08.047.
[7] T . Li, S .M. Fei, Q .Zhu, S .Song. Exponential synchronization of chaotic neural networks with mixed delays, Neurocomputing (2008), doi:10.1016/j.neucom.2007.12.029.
[8] J .Yan, J .Lin, M .Hung, T .Liao. On the synchronization of neural networks containing time-varying delays and sector nonlinearity, Phys. Lett. A, 2007, 361: 70-77.
[9] Y .Dai, Y .Z. Cai, X .M. Xu. Synchronization and Exponential Estimates of Complex Networks with Mixed Time-varying Coupling Delays. Int. Jour. Auto. Comput.,, 2007, 4(1): 100-106.
[10] Y .Q. Yang, J .D. Cao. Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects. Physica A, 2007, 386: 492-502.
[11] W .Yu, J .D. Cao. Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Phys. Lett. A,, 2007, 375: 467-482
[12] Q .J. Zhang, J .A. Lu. Chaos synchronization of a new chaotic system via nonlinear control. Chaos, Solitons and Fractals, 2008, 37: 175-179
[13] H .G. Zhang, Y .H. Xie, Z .L. Wang. Adaptive synchronization between two different chaotic neural networks with time delay. IEEE Transaction on Neural Networks, 2007, 18: 1841-1845.
[14] C.T.H. Baker, E. Buckwar. Exponential stability in pth mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations. J. Comput. Appl. Math, 2005, 184: 404-427.
[15] J .W. Luo. A note on exponential stability in pth mean of solutions of stochastic delay differential equations. J. Comput. Appl. Math, 2007, 198: 143-148.
[16] Z .G. Yang, D .Y. Xu, L .Xiang. Exponential p-stability of impulsive stochastic differential equations with delays. Phys. Lett. A, 2006, 359: 129-137.
[17] X .R. Mao. Exponential stability in mean square of neutral stochastic differential functional equations. Sys. Contr.Lett, 1995, 26: 245-251.
[18] X .R. Mao. Razumikhin type theorems on exponential stability of neutral stochastic functional differential equations. SIAM J. Math. Anal, 1997, 28(2): 389-401.
[19] J. Randjelovi'c, S. Jankovi'c. On the pth moment exponential stability criteria of neutral stochastic functional differential equations. J. Math. Anal. Appl, 2007, 326: 266-280.
[20] Y .H. Sun, J .D. Cao. pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. Nonlinear Anal: Real. world. Appl., 2007, 8: 1171-1185.
[21] L .Wan, J .Sun. Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A, 2005, 343:306-318.
[22] C .X. Huang, et al. pth moment stability analysis of stochastic recurrent neural networks with time-varying delays. Inf.Sci., 2008, 178: 2194-2203.
[23] S .J. Wu, D .Han, X .Z. Meng. p-Moment stability of stochastic differential equations with jumps. J. Comput. Appl. Math, 2004, 152: 505-519.
[24] S .J. Wu, X .L. Guo, Y .Zhou. p-moment stability of functional differential equations with random impulsive. Comput. Math. Appl., 2006, 52: 1683-1694.
[25] H .J. Wu, J .T. Sun. p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching. Automatica, 2006, 42: 1753-1759.
[26] X .R. Mao. Stochastic Differential Equation and Application, Horwood Publishing, Chichester, 1997.
[27] D .Y. Xu,Z .Wei, S. J. Long. Global exponential stability of impulsive integro-differential equation. Nonlinear Analysis, 2006, 64: 2805-2816.