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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 dxidt=gi(t)[∫hi1(t)tdτ1ri1(t,τ1)…∫his(t)tfi(x1(τ1),x2(τ2),…,xs(τs))dτsris(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.