An Investigation on a Unique Solution of the Hopfield and the T-Model Neural Networks

Abstract

In this paper we propose a new method using the mathematical induction method to investigate the unique solution of the Hopfield and the T-Model neural networks. The new method, unlike the traditional energy function method, treats the Hopfield and the T-Model neural networks as the nonlinear equations of F^-1 (V)=WV+_??_ and investigated their unique solution. The nonlinear equations are similar to the dc equations of nonlinear transistor networks for which many important theorems on the unique solution have been presented. We develop the techniques to invistigate the unique solution of the Hopfield and the T-Model neural network and expect to derive many other useful theorems on the necessary and sufficient conditions for the networks (i. e. the equations) to have a unique solution. In order to verify these results, We give several simulation results on both models.