NONINVERTIBILITY AND RESONANCE IN DISCRETE-TIME NEURAL NETWORKS FOR TIME-SERIES PROCESSING

We present a computer-assisted study emphasizing certain elements of t he dynamics of artificial neural networks (ANNs) used for discrete tim e-series processing and nonlinear system identification. The structure of the network gives rise to the possibility of multiple inverses of a phase point backward in time; this is not possible for the continuou s-time system from which the time series are obtained, Using a two-dim ensional illustrative model in an oscillatory regime, we study here th e interaction of attractors predicted by the discrete-time ANN model ( invariant circles and periodic points locked on them) with critical cu rves. These curves constitute a generalization of critical points for maps of the interval (in the sense of Julia-Fatou); their interaction with the model-predicted attractors plays a crucial role in the organi zation of the bifurcation structure and ultimately in determining the dynamic behavior predicted by the neural network. (C) 1998 Published b y Elsevier Science B.V.