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 non-delayed 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.