具有混合变时滞的脉冲Cohen-Grossberg神经网络的指数同步

摘要/Abstract

摘要：

该文研究了一类具有混合变时滞的脉冲Cohen-Grossberg神经网络模型的指数同步问题. 通过构造适当的Lyapunov函数和利用反证法, 得到了简单而有效的指数同步判据. 最后, 通过一个实例的数值模拟来说明所得结果的有效性.

关键词: Cohen-Grossberg神经网络, 指数同步, 脉冲, 混合变时滞

Abstract:

In this paper, the exponential synchronization of Cohen-Grossberg neural networks with mixed time-varying delays and impulsive effects is investigated. Based on the contradiction method and constructing suitable Lyapunov function, some simple and useful criteria for the synchronization of considered network are obtained. Finally, a numerical example is given to show the effectiveness and feasibility of the proposed synchronization scheme.

Key words: Cohen-Grossberg neural network, Exponential synchronization, Impulsive effect, Mixed time-varying delay

中图分类号:

阿卜杜杰力力·阿卜杜热合曼, 蒋海军, 滕志东. 具有混合变时滞的脉冲Cohen-Grossberg神经网络的指数同步[J]. 数学物理学报, 2015, 35(3): 545-557.

Abdujelil Abdurahman, Jiang Haijun, Teng Zhidong. Exponential Synchronization for Impulsive Cohen-Grossberg Neural Networks with Mixed Time-Varying Delays[J]. Acta mathematica scientia,Series A, 2015, 35(3): 545-557.

参考文献

[1] Hopfield J. Neural networks and physical systems with emergent collective computational abilities. Proc National Academy Sci USA, 1982, 79: 2554-2562
[2] Kamp Y, Hasler M. Recursive Neural Networks for Associative Memory. New York: Wiley, 1990
[3] Gopalsamy K, He X. Stability in asymmetric Hopfield nets with transmission delays. Physica D, 1994, 76: 344-358
[4] Jiang H, Li Z, Teng Z. Boundedness and stability for nonautonomous cellular neural networks with delay. Phys Lett A, 2003, 306: 313-325
[5] Gopalsamy K. Stability of artificial neural networks with impulses. Appl Math Comput, 2004, 154: 783-813
[6] Wu Z, Park J H, Su H, Chu J. Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data. Nonlinear Dyn, 2012, 69(4): 2021-2030
[7] Lisena B. Exponential stability of Hopfield neural networks with impulses. Nonlinear Anal RWA, 2011, 12: 1923-1930
[8] Wu Z, Park J H. Synchronization of discrete-time neural networks with time delays subject to missing data. Neurocomputing, 2013, 122: 418-424
[9] Fang M, Park J H. Non-fragile synchronization of neural networks with time-varying delay and randomly occurring controller gain fluctuation. Appl Math Comp, 2013, 219: 8009-8017
[10] Cohen M A, Grossberg S. Absoulute stability of global pattern formation and parallel memory storage by competetive neural networks. IEEE Trans Syst Man Cybern, 1983, 13: 815-826
[11] Ye H, Michel A N, Wang K. Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Phys Rev E, 1995, 51: 2611-2618
[12] Chen T, Rong L. Delay-independent stability analysis of Cohen-Grossberg neural networks. Phys Lett A, 2003, 317: 436-449
[13] Gan Q. Adaptive synchronization of Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays. Commun Nonlinear Sci Numer Simulat, 2012, 17: 3040-3049
[14] Gan Q. Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control. Neural Netw, 2012, 31: 12-21
[15] Arik S, Orman Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays. Phys Lett A, 2005, 341: 410-421
[16] Liu J. Global exponential stability of Cohen-Grossberg neural networks with time-varying delays. Chaos Soliton Fract, 2005, 26: 935-945
[17] Jiang H, Cao J, Teng Z. Dynamics of Cohen-Grossberg neural networks with time-varying delays. Phys Lett A, 2006, 354: 414-422
[18] Bowong S. Stability analysis for the synchronization of chaotic systems with different order: Application to secure communications. Phys Lett A, 2004, 326: 102-113
[19] Feki M. An adaptive chaos synchronization scheme applied to secure communications. Chaos Soliton Fract, 2003, 18: 141-148
[20] Konnur R. Synchronization-based approach for estimating all model parameters of chaotic systems. Phys Rev E, 2003, 67: 027204
[21] Rangarajan G, Ding M. Stability of synchronized chaos in coupled dynamical systems. Phys Lett A, 2002, 296: 204-209
[22] Hu M, Xu Z. Adaptive feedback controller for projective synchronization. Nonlinear Anal RWA, 2008, 9: 1253-1260
[23] Hu C, Jiang H, Teng Z. Fuzzy impulsive control and synchronization of general chaotic system. Acta Appl Math, 2010, 109: 463-485
[24] Yang Z, Xu D. Stability analysis and design of impulsive control systems with time delay. IEEE Tran Automat Control, 2007, 52: 1448-1454
[25] Zochowski M. Intermittent dynamical control. Physical D, 2000, 145: 181-190
[26] Yu J, Hu C, Jiang H, Teng Z. Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control. Neurocomputing, 2011, 74: 1776-1782
[27] Cao J, Lu J. Adaptive synchronization of neural networks with or without time-varying delays. Chaos, 2006, 16: 013133, 6 pages
[28] Cheng C, Liao T, Yan J, Hwang C. Exponential synchronization of a class of neural networks with time-varying delays. IEEE Trans Syst Man Cybern, 2006, 36: 209-215
[29] Cui B, Lou X. Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Soliton Fract, 2009, 39: 288-294
[30] Gan Q, Xu R, Kang X. Synchronization of chaotic neural networks with mixed time delays. Commun Nonlinear Sci Numer Simulat, 2011, 16: 966-974
[31] Wang K, Teng Z, Jiang H. Adaptive synchronization of neural networks with time-varying delay and distributed delay. Physica A, 2008, 387: 631-642
[32] Jeong S C, Ji D H, Park J H, Won S C. Adaptive synchronization for uncertain chaotic neural networks with mixed time delays using fuzzy disturbance observer. Appl Math Comp, 2013, 219: 5984-5995
[33] Bai C. Global exponential stability and existence of periodic solution of Cohen-Grossberg type neural networks with delays and impulses. Nonlinear Anal RWA, 2008, 9: 747-761
[34] Li J, Yan J, Jia X. Dynamical analysis of Cohen-Grossberg neural networks with time-delays and impulses. Comput Math Appl, 2009, 58: 1142-1151
[35] Sheng L, Yang H. Exponential synchronization of a class of neural networks with mixed time-varying delays and impulsive effects. Neurocomputing, 2008, 71: 3666-3674
[36] Feng X, Zhang F, Wang W. Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects. Chaos Soliton Fract, 2011, 44: 9-16
[37] Yang Y, Cao J. Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects. Physica A, 2007, 386: 492-502
[38] Cheng C, Liao T, Hwang C. Exponential synchronization of a class of chaotic neural networks. Chaos Soliton Fract, 2005, 24: 197-206
[39] Zhu Q, Cao J. Adaptive synchronization of chaotic Cohen-Grossberg neural networks with mixed time delays. Nonlinear Dyn, 2010, 61: 517-534
[40] Chen Z. Complete synchronization for impulsive Cohen-Grossberg neural networks with delay under noise perturbation. Chaos Soliton Fract, 2009, 42: 1664-1669