New estimate on the domains of attraction of equilibrium points in continuous Hopfield neural networks

Abstract

This Letter addresses the qualitative properties of equilibrium points in continuous Hopfield neural networks. We derive a sufficient condition for an equilibrium point to be locally exponentially stable. We also present 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. In addition, these results neither depend on the monotonicity of the activation functions nor on coupling conditions between the neurons. Consequently, our results are of practical importance in the evaluation of performance of Hopfield associative memory networks.