A harmonic balance approach for the qualitative analysis of limit cycles occurring in CNNs

The characteristics of limit cycles in CNNs composed by a finite number of cells are investigated through a suitable harmonic balance technique. It is proved that for a CNN described by the template [a(-1), a(0), a(1)] such a technique leads to a set of no more than 6 nonlinear equations, regardless of the number of cells. The method allows to predict all the main features of spatio-temporal periodic oscillations and yields results that ale in good agreement with those observed by the time-simulation of the network.