Full-range cellular neural networks and differential variational inequalities

Abstract

We consider the full-range (FR) model of cellular neural networks (CNNs) in the ideal case where the neuron nonlinearities are hard-comparator functions with two unbounded vertical segments. The dynamics of FR-CNNs is rigorously analyzed by using theoretical tools from set-valued analysis and differential inclusions. The fundamental property proved in the paper is that FR-CNNs are equivalent to a special class of differential inclusions named differential variational inequalities. On this basis, a sound foundation to the dynamics of FR-CNNs is given, by establishing results on the existence and uniqueness of the solution starting at a given point, and on the existence of equilibrium points. Moreover, some fundamental results on trajectory convergence towards equilibrium points (complete stability) for reciprocal standard CNNs are extended to reciprocal FR-CNNs by using a generalized Lyapunov approach.