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Guaranteed attractivity of equilibrium points in a class of delayed neural networks. (English) Zbl 1154.34389

Summary: This paper addresses qualitative properties of equilibrium points in a class of delayed neural networks. We derive a sufficient condition for the local exponential stability of equilibrium points, and give an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons’ activation functions and the associated equilibrium point; hence, they are easily checkable. Another advantage of our results is that they neither depend on monotonicity of the activation functions nor on symmetry of the interconnection matrix. Our work has practical importance in evaluating the performance of the related associative memory. To our knowledge, this is the first time to present an estimate on the domains of attraction of equilibrium points for delayed neural networks.

MSC:

34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
92B20 Neural networks for/in biological studies, artificial life and related topics
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