Fundamental study: Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

Authors:
Zhiguo Yang;Daoyi Xu
Affiliations:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China;Yangtze Center of Mathematics, Sichuan University, Chengdu, 610064, China
Venue:
Theoretical Computer Science
Year:
2008

Citing 7
Cited 8

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Abstract

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results.