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Discrete Dynamics in Nature and Society
Volume 2006, Article ID 27941, 11 pages

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

1Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China
2Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 14 February 2006; Accepted 25 April 2006

Copyright © 2006 Fei-Yu Zhang and Hai-Feng Huo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.