ON THE DYNAMICS OF SMALL CONTINUOUS-TIME RECURRENT NEURAL NETWORKS

Dynamical neural networks are being increasingly employed in a variety of contexts, including as simple model nervous systems for autonomous agents. For this reason, there is a growing need for a comprehensive understanding of their dynamical properties. Using a combination of el ementary analysis and numerical studies, this article begins a systema tic examination of the dynamics of continuous-time recurrent neural ne tworks. Specifically, a fairly complete description of the possible dy namical behavior and bifurcations of one- and two-neuron circuits is g iven, along with a few specific results for larger networks. This anal ysis provides both qualitative insight and, in many cases, quantitativ e formulas for predicting the dynamical behavior of particular circuit s and how that behavior changes as network parameters are varied. Thes e results demonstrate that even small circuits are capable of a rich v ariety of dynamical behavior (including chaotic dynamics). An approach to understanding the dynamics of circuits with time-varying inputs is also presented Finally based on this analysis, several strategies for focusing evolutionary searches into fruitful regions of network param eter space are suggested.