ANALYSIS AND SYNTHESIS OF A CLASS OF DISCRETE-TIME NEURAL NETWORKS WITH NONLINEAR INTERCONNECTIONS

In the present paper, a qualitative analysis and a synthesis procedure for a class of discrete-time, synchronous neural networks with nonlin ear interconnections (of polynomial form) are presented. Networks gene rated by the present synthesis procedure have, in general, greater mem ory storage capacity than corresponding networks with a linear interco nnecting structure. The qualitative results that constitute the basis of the synthesis procedure include a simple stability test for the equ ilibrium points of the class of networks considered, Conditions under which such networks are globally stable have not been identified at th is time. To simplify the presentation, we confine ourselves to second- order polynomial network interconnections; however, the qualitative re sults and the synthesis procedure developed herein apply to networks w ith higher order polynomial interconnections as well.