Dynamics of a class of discrete-time neural networks and their continuous-time counterparts

The dynamical characteristics of continuous-time additive Hopfield-type neu ral networks are studied. Sufficient conditions are obtained for exponentia lly stable encoding of temporally uniform external stimuli. Discrete-time a nalogues of the corresponding continuous-time models are formulated and it is shown analytically that the dynamics of the networks are preserved by bo th continuous-time and discrete-time systems. Two major conclusions are dra wn from this study: firstly, it demonstrates the suitability of the formula ted discrete-time analogues as mathematical models for stable encoding of a ssociative memories associated with external stimuli in discrete time, and secondly, it illustrates the suitability of our discrete-time analogues as numerical algorithms in simulating the continuous-time networks. (C) 2000 I MACS. Published by Elsevier Science B.V. All rights reserved.