AVERAGED NEURAL NETWORKS

Cohen and Grossberg studied an almost gradient system of ordinary diff erential equations with application to neural networks and used a Liap unov function, together with an invariance principle, to show that som e equilibrium points attract solutions. Independently, Hopfield modele d a neural network by means of a system of ordinary differential equat ions which turn out to be a special case of the Cohen-Grossberg system , as pointed out by Cohen. In the Hopfield model it is clear thal the functions involved in the equations are averages and that current will flow through a synapse only ifa certain threshold is reached; however , none of the models take into account an averaging technique. Investi gators have been interested in sustained oscillations in neural networ ks and have produced them in computer simulations when there is a poin twise delay. The linearized systems with a delay have also exhibited s ustained oscillations. But our conjecture is that oscillations are not caused by a delay. This paper is intended to put substance to that co njecture by examining models with both pointwise and distributed delay s. None of the models have solutions with sustained oscillations.