Qualitative analysis of Hopfield neural nets with delays: Global and local results

It is well known that Hopfield neural networks without delays exhibit no oscillations and possess global stability (i.e., all trajectories tend to some equilibrium). In the present paper we show that if the bound τβ||T₂||<1 is satisfied, then a corresponding Hopfield neural network with delays τ>0, interconnection matrix T₂ associated with delays, and gain of the neurons given by β, will exhibit similar qualitative properties as the original Hopfield neural network without delays (||T₂ || denotes the matrix norm induced by the Euclidean vector norm)