A harmonic balance technique for the analysis of periodic attractors and their bifurcations in CNNs

Abstract

The occurrence of periodic attractors in CNNs is investigated through a harmonic balance technique. It is shown that for a N-cell CNN described by the template [a/sub -1/, a/sub 0/, a/sub 1/], this technique leads to a set of 3N nonlinear equations, that can be reduced to 2N+1 equations through suitable algebraic manipulations. The technique allows to determine all the limit cycles and most of the bifurcation phenomena occurring in the network. The results are in good agreement with those observed by the time-simulation of the network.