J. Si et An. Michel, ANALYSIS AND SYNTHESIS OF A CLASS OF DISCRETE-TIME NEURAL NETWORKS WITH NONLINEAR INTERCONNECTIONS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 41(1), 1994, pp. 52-58
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.