Finding all stable equilibria of cellular neural networks

Abstract

SUMMARYAn efficient algorithm is given for finding all stable equilibrium states of a cellular neural network. The method is based upon a new theorem concerning the network dynamics. The theorem implies the implementation of a simple sign test which, combined with a binary tree search, efficiently performs the task of searching the equilibria. Since the proposed algorithm uses information about the network architecture and dynamic behaviour, it exhibits two important advantages over other more general methods for searching the equilibria of resistive piecewise-linear circuits. First, the regions which cannot possibly include stable steady states can be eliminated even before starting to perform the algorithm. Secondly, there is no need to solve any set of linear equations, which is usually the most tedious part of equilibrium-searching methods.

Template design methods for binary stable cellular neural networks

“…For what concerns the ÿrst task, i.e. the computation of all the equilibrium points, some results are available in Reference [33] and especially in Reference [34], where an e cient algorithm is provided for determining all the stable equilibrium points. For what concerns the second task, i.e.…”