具时滞和脉冲的随机BAM型Cohen-Grossberg神经网络的稳定性分析

摘要/Abstract

摘要：

大多数的随机神经网络文章中很少考虑脉冲的影响, 该文利用分析方法、拓扑度的同伦不变性、It\^o公式及M 矩阵相关理论,
研究了一类具有时滞和脉冲随机神经网络的指数稳定性. 文章推广了以往文献的结果, 并通过实例验证了结论的实用性.

Abstract:

In most papers, stochastic neural network with impulse is studied rarely. In this paper, we consider the global exponential stability of a class of BAM-type Cohen-Grossberg neural networks with delay, impulse and stochastic disturbance by It\^{o} differential formula, M-matrix theory, homotopic invariance theorem and stochastic analysis technique and so on. This paper extends other previous results, and an example is given to show the effectiveness of the results obtained here.

Key words: Neural network, Impulse, Stochastic, Stability

中图分类号:

93D20

潘特铁, 时宝, 杨树杰, 张强. 具时滞和脉冲的随机BAM型Cohen-Grossberg神经网络的稳定性分析[J]. 数学物理学报, 2013, 33(5): 937-950.

PAN Te-Tie, SHI Bao, YANG Shu-Jie, ZHANG Qiang. Stability Analysis of Stochastic BAM-type Cohen-Grossberg Neural Networks with Delays and Impulses[J]. Acta mathematica scientia,Series A, 2013, 33(5): 937-950.

参考文献

[1]  Cohen M A, Grossberg S. Absolute stability and globle pattern formation and parallel memory storage by competitive neural networks. IEEE Trans on Syst Man and Cybern, 1983, 13(5): 815--826

[2] Li Y K, Fan X L. Existence and globally exponential stability of almost periodic solution for Cohen-Grossberg BAM neural networks with variable coefficients. Appl Math Model, 2009, 33(4): 2114--2120

[3] 张丽娟. !Existence and global attractivity of almost periodic solution for BAM neural networks with variable coefficients and delays. 生物数学学报, 2007, 22(3): 403--412

[4] Xiang H J, Cao J D. Almost periodic solution of Cohen-Grossberg neural networks with bounded and unbounded delays. Nonlinear Anal-Real, 2009, 10(4): 2407--2419

[5] Chen Z, Ruan J. Global stability analysis of impulsive Cohen-Grossberg neural networks with delay. Phys Lett A,
2005, 345(1--3): 101--111

[6] Rakkiyappan R, Balasubramaniam P, Cao J D. Global exponential stability results for neutral-type impulsive neural networks. Real World Appl, 2010, 11(1): 122--130

[7] Li K L, Zeng H L. Stability in impulsive Cohen-Grossberg-type BAM neural networks with time-varying delays:  a general analysis. Math Comput Simulat, 2010, 80(3): 2329--2349

[8] Li K L. Delay-dependent stability analysis for impulsive BAM neural networks with time-varying delays. Comput Math Appl, 2008, 56(8): 2088--2099

[9] Zhou Q H, Wan L. Impulsive effects on stability of Cohen-Grossberg-type bidirectional associative memory neural networks with delays. Nonlinear Anal-Real, 2009, 10(4): 2531--2540

[10] Li Y T, Yang C B. Global exponential stability analysis on impulsive BAM neural networks with distributed delays. J Math Anal Appl, 2006, 324(2): 1125--1139

[11] Zhao H Y, Ding N. Dynamic analysis of stochastic bidirectional sociative memory neural networks with delays. Chaos Solit Fract, 2007, 32(5): 1692--1702

[12] Zhao H Y, Ding N. Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays. Appl Math Comput, 2006, 183(1): 464--470

[13] Hu J, Zhong S M, Liang L. Exponential stability analysis of  stochastic delayed cellular neural network. Chaos Solit Fract, 2006, 27(4): 1006--1010

[14] Zhou Q H, Wan L. Exponential stability of stochastic delayed Hopfield neural networks. Appl Math Comput, 2008, 199(1): 84--89

[15] Huang C X, Cao J D. On $P$th moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays. Neurocomputing, 2010, 73(4--6): 986--990

[16] Zhu E W, Zhang H M, Wang Y, et al. Pth moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays. Neural Process Lett, 2007, 26(3): 191--200

[17] Huang C X, He Y G, Chen P. Dynamic analysis of stochastic recurrent neural networks. Neural Process Lett, 2008, 27(3): 267--276

[18] Song Q K, Wang Z D. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Physica A, 2008, 387(13): 3314--3326

[19] Lu J X, Duan X B, Fu R. The p-moment stability for stochastic hopfield-type neural networks with impulses. Chinese J Engineering Mathematics, 2010, 27(4): 741--746

[20] Huang C X, He Y G, Wang H N. Mean square exponential stability of stochastic recurrent neural networks with time-varying delays. Comput Math Appl, 2008, 56(7): 1773--1778

[21] 胡适耕, 黄乘明, 吴付科. 随机微分方程. 北京: 科学出版社, 2008

[22] Zhang C L, Yang F J, Hu X J. Global exponential stability of BAM neural networks with varying coefficient impulses. J Biomathematics, 2007, 22(3): 395--402

[23] Xia Y H, Huang Z K, Han M A. Exponential p-stability of delayed Cohen-Grossberg-type BAM neural networks with impulses. Chaos Soliton Fract, 2008, 38(3): 806--818

[24] Lou X Y, Cui B T. Global asymptotic stability of delay BAM neural networks with impulses based on matrix theory. Appl Math Model, 2008, 32(2): 232--239

[25] Wen Z, Sun J T. Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis. Neurocomputing, 2008, 71(7--9): 1543--1549

[26] Ahmad Shair, Stamova Ivanka M. Global exponential stability for impulsive cellular neural networks with time-varying delays. Nonlinear Anal-Theo, 2008, 69(3): 786--795

[27] Xia Y H, Wong Patricia J Y. Global exponential stability of a class of retarded impulsive differential equations with applications. Chaos Soliton Fract, 2009, 39(1): 440--453

[28] Yang F J, Zhang C L, Wu D Q. Global stability analysis of impulsive BAM type Cohen-Grossberg neural networks with delays. Appl Math Comput, 2007, 186(1): 932--940

[29] Bai C Z. Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses. Chaos Soliton Fract, 2008, 35(2): 263--267

[30] Xia Y H, Huang Z K, Han M A. Existence and globally exponential stability of equilibrium for BAM neural networks with impulses. Chaos Soliton Fract, 2008, 37(2): 588--597

[31] Huang Z K, Xia Y H. Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses. Chaos Soliton Fract, 2008, 38(2): 489--498