The Stability Research For A Class Of Static Neural Networks

This paper analyzes the stability for a class of static recurrent neural networks with delays. The paper has three parts.In the first chapter, the background, the meaning and the general development of the researched issue are introduced.In the second chapter, the stability for a new class of static recurrent neural networks with delays Pis studied. By using properties of M-matrix, method of Liapunov function, inequality technique and the topological degree theory, the paper investigates the global robust stability, the global exponential stability, invariant sets and gloable attracting sets. Some conditions of activation function given in this paper are weaker than those given in quoted articles, and some known results are generalized. At last, the computer simulation by MATLAB have shown its feasibilityIn the third chapter, the multistability for a class of static neural network Pis studied via a geometrical observation. The existence domains of multiple quilibria are given, and also the spatial location of positive invariant set is estimated.