Synthesis techniques for discrete time neural network models

The authors establish a qualitative theory for synchronous, discrete-time, Hopfield-type neural networks. Their objectives are accomplished in two phases. They analyze the class of neural networks considered and use the results to develop a synthesis procedure for them. The analysis utilizes techniques from the theory of large-scale interconnected dynamical systems to derive tests for the asymptotic stability of an equilibrium of the neural network. Estimates are obtained for the rate at which the trajectories of the network will converge from an initial condition to a final state. The authors utilize the stability tests as constraints to develop a design algorithm for content-addressable memories. The algorithm guarantees that each desired memory will be stored as an equilibrium and will be asymptotically stable. The applicability of the results is demonstrated for a 13-neuron and for an 81-neuron network