Global asymptotic stability for neural network models with distributed delays

Abstract

In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the nondelayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well known neural network models of Hopfield, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.