Synchronization for Impulsive Fuzzy Cohen-Grossberg Neural Networks with Time Delays under Noise Perturbation

Authors: Changzhao Li, Juan Zhang

Abstract:

In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.

Keywords: Fuzzy Cohen-Grossberg neural networks (FCGNNs), complete synchronization, time delays, impulsive, noise perturbation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062386

References:

[1] M. Cohen, S. Grossberg, Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst., Man., Cybern. 13 (1983) 815-826.
[2] Z. Zhang, D. Zhou, Global robust exponential stability for second-order Cohen-Grossberg neural networks with multiple delays, Neurocomputing 73 (1-3) (2009) 213-218.
[3] Y. Li, X. Fan, Existence and globally exponential stability of almost periodic solution for Cohen-Grossberg BAM neural networks with variable coefficients, Appl. Math. Model. 33 (4) (2009) 2114-2120.
[4] Q. Zhu, J. Cao, Exponential stability analysis of stochastic reactiondiffusion Cohen-Grossberg neural networks with mixed delays, Neurocomputing (In Press), doi: 10.1016/j.neucom.2011.04.030.
[5] Jos'e J. Oliveira, Global stability of a Cohen-Grossberg neural network with both time-varying and continuous distributed delays , Nonlinear Analysis: R. W. A., 12 (5) (2011) 2861-2870.
[6] T. Yang, L. B. Yang, C. W. Wu, L. O. Chua, Fuzzy cellular neural networks: theory, in: Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications, (1996) 181-186.
[7] L. Chen, R. Wu, D. Pan, Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays, Exp. Sys. Appl., 38 (5) (2011) 6294-6299.
[8] P. Balasubramaniam, M. Kalpana, R. Rakkiyappan, Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays, Math. Comp. Mode. 53 (5-6) (2011) 839-853.
[9] W. Ding, M. Han, M. Li, Exponential lag synchronization of delayed fuzzy cellular neural networks with impulses, Phys. Lett. A, 373 (2009) 832-837.
[10] L. Pecora, T. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990) 821-824.
[11] W. Ding, M. Han, Synchronization of delayed fuzzy cellular neural networks based on adaptive control, Phys. Lett. A, 372 (2008) 4674-4681.
[12] W. Ding, Synchronization of delayed fuzzy cellular neural networks with impulsive effects, Commun Nonlinear Sci Numer Simulat 14 (2009) 3945-3952.
[13] F. Yu, H. Jiang, Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms, Neurocomputing 74 (2011) 509-515.
[14] Q. Gan, R. Xu, P. Yang, Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control, Commun Nonlinear Sci Numer Simulat (In Press), doi:10.1016/j.cnsns.2011.05.014.
[15] Z. Wang, L. Huang, Y. Wang, Y. Zuo, Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method, Commun Nonlinear Sci Numer Simulat 15 (2010) 4202-4208.
[16] C. Li, W. Sun, J. Kurths, Synchronization of complex dynamical networks with time-delays, Physica A 361 (2006) 24-34.
[17] W. He, J. Cao, Exponential synchronization of chaotic neural networks: a matrix measure approach, Nonlinear Dyn. 55(1) (2009) 55-65.
[18] Y. Wu, C. Li, Y. Wu, J. Kurths, Generalized synchronization between two different complex networks, Commun Nonlinear Sci Numer Simulat (In Press), doi:10.1016/j.cnsns.2011.04.026.
[19] Y. Xia, Z. Yang, M. Han, Lag synchronization of unknown chaotic delayed yang-yang-type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification, IEEE Trans. Neural Networks 20 (7) (2009) 1165-1180.
[20] Y. Sun, J. Cao, Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation, Phys. Lett. A 364 (2007) 277-285.
[21] C. Masoller, Anticipation in the synchronization of chaotic time-delay systems, Physica A 295 (2001) 301-304.
[22] Y. Kuang, Delay differential equations with applications in population dynamics, Acedemic press, New York, 1993.
[23] C. Li, Y. Li, Y. Ye, Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Commun Nonlinear Sci Numer Simulat 15 (2010) 3599-3606.
[24] J. Zhou, L. Xiang, Z. Liu, Synchronization in complex delayed dynamical networks with impulsive effects, Physica A 384 (2007) 684-92.
[25] Z. Chen, Complete synchronization for impulsive Cohen-Grossberg neural networks with delay under noise perturbation, Chaos, Solitons and Fractals 42 (2009) 1664-1669.
[26] Y. Sun, J. Cao, Z. Wang, Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing 70 (2007) 2477-2485.
[27] A. Friedman, Stochastic differential equations and applications, Academic Press, New York, 1976.