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

The dynamical characteristics of continuous-time additive Hopfield-type neural networks are studied. Sufficient conditions are obtained for exponentially stable encoding of temporally uniform external stimuli. Discrete-time analogues of the corresponding continuous-time models are formulated and it is shown analytically that the dynamics of the networks are preserved by both continuous-time and discrete-time systems. Two major conclusions are drawn from this study: firstly, it demonstrates the suitability of the formulated discrete-time analogues as mathematical models for stable encoding of associative 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.