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 nonlinear interconnections (of polynomial form) are presented. Networks generated by the present synthesis procedure have, in general, greater memory storage capacity than corresponding networks with a linear interconnecting structure. The qualitative results that constitute the basis of the synthesis procedure include a simple stability test for the equilibrium points of the class of networks considered. Conditions under which such networks are globally stable have not been identified at this time. To simplify the presentation, we confine ourselves to second-order polynomial network interconnections; however, the qualitative results and the synthesis procedure developed herein apply to networks with higher order polynomial interconnections as well.