Convergence Criteria for a Hopfield-type Artificial Neural Network

Abstract

Motivated by recent applications of the Lyapunov method in artificial neural networks, which could be considered as dynamical systems for which the convergence of system trajectories to equilibrium states is a necessity, we re-look at a well-known Krasovskii stability criterion pertaining to autonomous systems and then essentially use the same underlying idea to propose appropriate convergence criteria for autonomous system. We then apply the criteria to neural networks and discuss our results with respect to recent ones in the field.