Qualitative analysis of artificial neural networks with multiple delays

It is well known that a class of artificial neural networks with symmetric interconnections and without transmission delays, known as Cohen-Grossberg neural networks, possesses global stability (i.e., all trajectories tend to some equilibrium). The authors demonstrate in the present paper that many of the qualitative properties of Cohen-Grossberg networks will not be affected by the introduction of sufficiently small delays. Specifically, the authors establish some bound conditions for the time delays under which a given Cohen-Grossberg network with multiple delays is globally stable and possesses the same asymptotically stable equilibria as the corresponding network without delays. An effective method of determining the asymptotic stability of an equilibrium of a Cohen-Grossberg network with multiple delays is also presented