In this chapter we review various computational models of locally recurrent neurons and deliberate the architecture of some archetypal locally recurrent neural networks (LRNNs) that are based on them. Generalizations of these structures are discussed as well. Furthermore, we point at a number of realworld applications of LRNNs that have been reported in past and recent publications. These applications involve classification or prediction of temporal sequences, discovering and modeling of spatial and temporal correlations, process identification and control, etc. Validation experiments reported in these developments provide evidence that locally recurrent architectures are capable of identifying and exploiting temporal and spatial correlations (i.e., the context in which events occur), which is the main reason for their advantageous performance when compared with the one of their non-recurrent counterparts or other reasonable machine learning techniques.
Local stability conditions for discrete-time cascade locally recurrent neural networks