Counting stable equilibria of cellular neural networks-A graph theoretic approach

A graph-theoretic method for computation of the number of stable equilibrium points and analysis of the structure of the cellular neural network (CNN) equilibrium set is presented. The considerations are based on one-dimensional CNN layout. The total number of these equilibria, referred to as output capacity, is shown to be equal to the number of paths in a graph derived from neighborhood consistency conditions. It may vary vastly depending on interaction weights and bias current of the cells. The author points out that output capacity equal to zero implies oscillations of the CNN state