Existence and Stability of Non-zero Steady State Solutions for Discrete Neutral Networks

In this paper, a neural networks model is established. The existence of non-zero solution pairs for its steady state equation and the local asymptotically stability of non-zero solutions are studied by using the critical point theory, Lusternik-Schnirelmann category theory, and the linearization technology. The similar method can be also used for the more general neural networks and the coupled map lattice system.