Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 673548, 10 pages
doi:10.1155/2009/673548
Research Article

Stability Analysis of Discrete Hopfield Neural Networks with the Nonnegative Definite Monotone Increasing Weight Function Matrix

Jun Li,1 Yongfeng Diao,2 Mingdong Li,3 and Xing Yin1

1School of Computer Science and Technology, Pan Zhi Hua University, Panzhihua 637000, China
2Teaching Affairs Office, China West Normal University, Nanchong 637002, China
3School of Computer Science, China West Normal University, Nanchong 637002, China

Received 12 February 2009; Accepted 3 July 2009

Academic Editor: Guang Zhang

Copyright © 2009 Jun Li et al. 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.

Abstract

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix (DHNNWFM) the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix (WFM) is weakly (or strongly) nonnegative definite function matrix, the DHNNWFM will converge to a stable state in serial (or parallel) model, and if WFM consisted of strongly nonnegative definite function matrix and column (or row) diagonally dominant function matrix, DHNNWFM will converge to a stable state in parallel model.