Critical dynamics study on recurrent neural networks: Globally exponential stability

Critical dynamics research of recurrent neural networks (RNNs) is very meaningful in both theoretical importance and practical significance. Due to the essential difficulty in analysis, there were only a few contributions concerning it. In this paper, we devote to study the critical dynamics behaviors for RNNs with general forms. By exploring some intrinsic features processed naturally by the nonlinear activation mappings of RNNs, and by using matrix measure theory, new criteria are found to ascertain the globally exponential stability of RNNs under the critical conditions. The results obtained here either yield new, or sharpen, extend or unify, to a large extent, most of the existing non-critical conclusions as well as the latest critical results.