AAM  >> Vol. 3 No. 2 (May 2014)

    随机Hopfield神经网络渐进行为的变互式凸组合方法
    Reciprocally Convex Approach to Asymptotic Behavior of Stochastic Hopfield Neural Networks

  • 全文下载: PDF(636KB) HTML    PP.70-77   DOI: 10.12677/AAM.2014.32011  
  • 下载量: 1,274  浏览量: 5,188  

作者:  

陈无及,李青松:长沙理工大学数学与计算科学学院,长沙

关键词:
Hopfield神经网络有界性均方指数稳定变互式凸组合方法Hopfield Neural Networks Boundedness Mean Square Exponential Stability Reciprocally Convex Approach

摘要:

本文通过构造合适Lyapunov-Krasovskii泛函,采用变互式凸组合方法、自由权矩阵方法、随机分析技巧、线性矩阵不等式(LMI)方法,研究了一类随机Hopfield神经网络的随机一致最终有界性、随机吸引子的存在性以及均方指数的稳定性。我们得到了随机Hopfield神经网络的新的结果和时滞依靠的充分条件。最后,应用MATLAB数值模拟检验来得到了理论的有效性。

In this paper, the problems of stochastic uniformly ultimate boundedness, the existence of stochastic attractor and mean square exponential stability for stochastic Hopfield neural networks are studied by constructing proper Lyapunov-Krasovskii functional, utilizing the reciprocally con- vex approach, the free-weighting matrix method, some stochastic analysis techniques and linear matrix inequalities technique (LMI). We deduce novel results and delay-dependent sufficient conditions for stochastic Hopfield neural networks. Finally, numerical simulations are given on MATLAB to verify the effectiveness of the gained results.

文章引用:
陈无及, 李青松. 随机Hopfield神经网络渐进行为的变互式凸组合方法[J]. 应用数学进展, 2014, 3(2): 70-77. http://dx.doi.org/10.12677/AAM.2014.32011

参考文献

[1] Ogura, H., Agata, H., Xie, M., et al. (1997) A study of learning splice sites of DNA sequence by neural networks. Computers in Biology and Medicine, 27, 67-75.
[2] Waibel, A., Hanazawa, T., Hinton, G., et al. (1989) Phoneme recognition using time-delay neural networks. IEEE Transactions on Acoustics, Speech and Signal Processing, 37, 328-339.
[3] Basu, J.K., Bhattacharyya, D. and Kim, T. (2010) Use of artificial neural network in pattern recognition. International Journal of Software Engineering & Its Applications, 4.
[4] Lam, J., Xu, S., Ho, D.W.C., et al. (2012) On global asymptotic stability for a class of delayed neural networks. Inter- national Journal of Circuit Theory and Applications, 40, 1165-1174.
[5] Lou, X., Ye, Q. and Cui, B. (2012) Stabilization analysis of stochastic Hopfield neural networks. 2012 12th IEEE In- ternational Conference on Control, Automation and Systems (ICCAS), 930-933.
[6] Wan, L. and Zhou, Q. (2011) Attractor and ultimate boundedness for stochastic cellular neural networks with delays. Nonlinear Analysis: Real World Applications, 12, 2561-2566.
[7] Cao, J. and Liang, J. (2004) Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. Journal of Mathematical Analysis and Applications, 296, 665-685.
[8] Park, P.G., Ko, J.W. and Jeong, C. (2011) Reciprocally convex approach to stability of systems with time-varying de- lays. Automatica, 47, 235-238.