Convergence Criteria for a Hopfield-type Neural Network

Motivated by recent applications of the Lyapunov's method in artificial neural networks, which could be considered as dynamical systems for which the convergence of the system trajectories to equilibrium states is a necessity. We re-look at a well-known Krasovskii's stability criteria pertaining to a non linear autonomous system. Instead, we consider the components of the same autonomous system with the help of the elements of Jacobian matrix J(x), thus proposing much simpler convergence criteria via the method of Lyapunov. We then apply our results to artificial neural networks and discuss our results with respect to recent ones in the field.