Analysis and synthesis of a class of discrete-time neural networks described on hypercubes

A qualitative analysis is presented for a class of synchronous discrete-time neural networks defined on hypercubes in the state space. Analysis results are utilized to establish a design procedure for associative memories to be implemented on the present class of neural networks. To demonstrate the storage ability and flexibility of the synthesis procedure, several specific examples are considered. The design procedure has essentially the same desirable features as the results of J. Li et al. (1988, 1989) for continuous-time neural networks. For a given system dimension, networks designed by the present method may have the ability to store more patterns (as asymptotically stable equilibria) than corresponding discrete-time networks designed by other techniques. The design method guarantees the storage of all the desired patterns as asymptotically stable equilibrium points. The present method provides guidelines for reducing the number of spurious states and for estimating the extent of the patterns' domains of attraction. The present results provide a means of implementing neural networks by serial processors and special digital hardware.