Synchronization for Impulsive Fuzzy Cohen-Grossberg Neural Networks with Time Delays under Noise Perturbation
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062386Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 W. Ding, M. Han, M. Li, Exponential lag synchronization of delayed fuzzy cellular neural networks with impulses, Phys. Lett. A, 373 (2009) 832-837.
 L. Pecora, T. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990) 821-824.
 W. Ding, M. Han, Synchronization of delayed fuzzy cellular neural networks based on adaptive control, Phys. Lett. A, 372 (2008) 4674-4681.
 W. Ding, Synchronization of delayed fuzzy cellular neural networks with impulsive effects, Commun Nonlinear Sci Numer Simulat 14 (2009) 3945-3952.
 F. Yu, H. Jiang, Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms, Neurocomputing 74 (2011) 509-515.
 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.
 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.
 C. Li, W. Sun, J. Kurths, Synchronization of complex dynamical networks with time-delays, Physica A 361 (2006) 24-34.
 W. He, J. Cao, Exponential synchronization of chaotic neural networks: a matrix measure approach, Nonlinear Dyn. 55(1) (2009) 55-65.
 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.
 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.
 Y. Sun, J. Cao, Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation, Phys. Lett. A 364 (2007) 277-285.
 C. Masoller, Anticipation in the synchronization of chaotic time-delay systems, Physica A 295 (2001) 301-304.
 Y. Kuang, Delay differential equations with applications in population dynamics, Acedemic press, New York, 1993.
 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.
 J. Zhou, L. Xiang, Z. Liu, Synchronization in complex delayed dynamical networks with impulsive effects, Physica A 384 (2007) 684-92.
 Z. Chen, Complete synchronization for impulsive Cohen-Grossberg neural networks with delay under noise perturbation, Chaos, Solitons and Fractals 42 (2009) 1664-1669.
 Y. Sun, J. Cao, Z. Wang, Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing 70 (2007) 2477-2485.
 A. Friedman, Stochastic differential equations and applications, Academic Press, New York, 1976.