Analysis and Synthesis of a Class of Discrete-Time Neural Networks Described on Hypercubes

In this paper, we first present a qualitative analysis for a class of synchronous discrete-time neural networks defined on hypercubes in the state space. Next, we utilize these analysis results to establish a design procedure for associative memories to be implemented by the present class of neural networks. To demonstrate the storage ability and flexibility of our synthesis procedure, several specific examples are considered. The present design procedure has essentially the same desirable features as our earlier results 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 present design method guarantees to store all of the desired patterns as asymptotically stable equilibrium points; and the present method provides guidelines for reducing the number of spurious states and for estimating the extent of the domains of attraction for the patterns to be stored as asymptotically stable equilibrium points. In addition, the present results provide a means of implementing neural networks by serial processors and special digital hardware. Thus, the present results make possible efficient digital simulations of continuous-time neural networks designed by the present method.