Complete stability for a class of cellular neural networks

Abstract

This work investigates a class of lattice dynamical systems originated from cellular neural networks. In the vector field of this class, each component of the state vector and the output vector is related through a sigmoidal nonlinear output function. For two types of sigmoidal output functions, Liapunov functions have been constructed in the literatures. Complete stability has been studied for these systems using LaSalle's invariant principle on the Liapunov functions. The purpose of this presentation is two folds. The first one is to construct Liapunov functions for more general sigmoidal output functions. The second is to extend the interaction parameters into a more general class, using an approach by Fiedler and Gedeon. This presentation also emphasizes the complete stability when the equilibrium is not isolated for the standard cellular neural networks.