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

Abstract

We consider a system of s nonlinear differential equations with a distributed] 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.

On stability of equations with an infinite distributed delay

“…Is it equivalent to global attractivity, as the case is still one-dimensional? (v) A natural extension of the main results of the present paper would be proceeding to the vector analogue of equation (1.1) in the spirit of [4].…”

Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks

“…The global stability criterion established for the general nonautonomous differential system, (1.5), including nonlinear terms with possible unbounded delays and linear terms with finite delay, Theorem 3.3. We remark that, recently, T. Faria [14] obtained global stability criteria for delay linear systems, while Berezansky and Braverman [6] obtained a global stability criterion for a general nonautonomous delay differential system, but with no delays in the linear terms;…”