Discrete Dynamics in Nature and Society 
Volume 2006 (2006), Article ID 27941, 11 pages
doi:10.1155/DDNS/2006/27941

Global stability of Hopfield neural networks under dynamical thresholds with distributed delays

Fei-Yu Zhang1 and Hai-Feng Huo2

 1Department of Mathematics, Hexi University, Zhangye 734000, Gansu, China
2Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
Received 14 February 2006; Accepted 25 April 2006

Abstract

We study the dynamical behavior of a class of Hopfield neural networks with distributed delays under dynamical thresholds. Some new criteria ensuring the existence, uniqueness, and global asymptotic stability of equilibrium point are derived. In the results, we do not require the activation functions to satisfy the Lipschitz condition, and also not to be bounded, differentiable, or monotone nondecreasing. Moreover, the symmetry of the connection matrix is not also necessary. Thus, our results improve some previous works in the literature. These conditions have great importance in designs and applications of the global asymptotic stability for Hopfield neural networks involving distributed delays under dynamical thresholds.