On the global attractivity of non-autonomous neural networks with a distributed delay

We consider a system of s nonlinear differential equations with a distributed delay dxi dt = gi(t)[ ∫t hi1(t) dτ1 ri1(t, τ1) . . . ∫t his(t) fi(x1(τ1), x2(τ2), . . . , xs(τs))dτs ris(t, τs) - xi(t)] and obtain global asymptotic stability conditions, which are independent of delays. The ideas of the proofs are based on the notion of a strong attractor of a vector difference equation associated with a nonlinear vector differential equation. The results are applied to Hopfield neural networks and to compartment-type models of population dynamics with Nicholson's blowflies growth law.