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Discrete Dynamics in Nature and Society
Volume 2005, Issue 1, Pages 1-17

Global stability of delayed Hopfield neural networks under dynamical thresholds

1Department of Mathematics, Hexi University, Gansu, Zhangye 734000, China
2Department of Mathematics, Lanzhou University, Gansu, Lanzhou 730000, China

Received 16 July 2004

Copyright © 2005 Hindawi Publishing Corporation. 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 dynamical behavior of a class of cellular neural networks system with distributed delays under dynamical thresholds. By using topological degree theory and Lyapunov functions, some new criteria ensuring the existence, uniqueness, global asymptotic stability, and global exponential stability of equilibrium point are derived. In particular, our criteria generalize and improve some known results in the literature.