Existence and stability of equilibria of the continuous-time Hopfield neural network

Authors:
Shihua Chen;Qin Zhang;Changping Wang
Affiliations:
College of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;College of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;Department of Mathematics and Statistics, Dalhousie University, Halifax NS, Canada B3H 3J5
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

The qualitative properties of the continuous-time Hopfield neural network are investigated. By using the Cauchy existence theorem of ordinary differential equations, a set of new and simple sufficient conditions guaranteeing the existence and uniqueness of equilibrium is derived. Furthermore, global and asymptotical stability conditions are established by means of Lyapunov method.