Without Diagonal Nonlinear Requirements: The More General -Critical Dynamical Analysis for UPPAM Recurrent Neural Networks

Continuous-time recurrent neural networks (RNNs) play an important part in practical applications. Recently, due to the ability of assuring the convergence of the equilibriums on the boundary line between stable and unstable, the study on the critical dynamics behaviors of RNNs has drawn especial attentions. In this paper, a new asymptotical stable theorem and two corollaries are presented for the unified RNNs, that is, the UPPAM RNNs. The analysis results given in this paper are under the generally -critical conditions, which improve substantially upon the existing relevant critical convergence and stability results, and most important, the compulsory requirement of diagonally nonlinear activation mapping in most recent researches is removed. As a result, the theory in this paper can be applied more generally.