时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性

基金项目: 国家自然科学基金资助项目(19771059);四川省教委基金

Global Attractivity and Global Exponential Stability for Delayed Hopfield Neural Network Models

1.
Department of Mathematics, Sichuan Normal University, Chengdu 610066, P R China;
2.
Department of Mathematics, Sichuan University, Chengdu 610064, P R China

摘要: 对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全局吸引和平衡点全局指数稳定的易于验证的充分条件。
- 神经网络 /
- 全局吸引 /
- 全局指数稳定
Abstract: Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model,under the weaker assumptions on nonlinear activation functions,are concerned.By constructing suitable Liapunov function,some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural networks with time delays are presented.
- neural networks /
- global attractivity /
- global exponential stability

[1]	Hopfield J J. Neurons with graded response have collective computational properties like those of two-stage neurons[J]. Proc Nat Acad Sci,1984,81(10):3088-3092.
[2]	张立明. 人工神经网络的模型及其应用[M]. 上海:复旦大学出版社,1993.
[3]	Goplasam K, He X. Stability in asymmetric hopfield nets with transmission delays[J]. Phys D,1994,76(4):344-358.
[4]	Makucus C M, Westervelt R M. Stability of analog neural networks with asymmetric connection weights[J]. Phys Rev A,1989,39(1):347-359.
[5]	Tank D, Hopfield J J. Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming network [J]. IE EE Trans Circuits Systems,1986,33(5):533-541.
[6]	Van Den Driessche P, Zou X. Global attractivity in delayed hopfield neural networks models[J]. SIAM J Appl Math,1998,58(6) :1878-1890.
[7]	Matsuoka K. Stability conditions for nonlinear continuous networks with asymmetric connection weights[J]. Netural Neworks,1992,5(3):495-500.
[8]	梁学斌,吴立德. Hopfield型神经网络的全局指数稳定性及其应用[J]. 中国科学(A辑),1995,25(5):523-532.
[9]	梁学斌,吴立德. 关于Hopfield型神经网络的全局指数稳定性[J]. 科学通报,1996,41(15):1434-1438.
[10]	Morita M. Associative memory with non-monotone dynamics[J]. Neural Networks,1993,6(1):115-126.