Dynamics analysis for generic projection continuous-time RNNs with bounded matrices

Abstract

The dynamics analysis of recurrent neural networks (RNNs) is a first and necessary step for any practical applications of them. In the present paper, the easily verified theorem is found to as certain the asymptotical stability for generic RNN model with projection mapping under the critical condition that a discriminant matrix defined by the networks is semi-positive definite. The results given here not only improve deeply upon the existing relevant critical as well as non-critical dynamics conclusions in literature, but also can be used in the practical application of RNNs directly.