ANALYSIS OF PERIODIC OSCILLATIONS IN FINITE-DIMENSIONAL CNNS THROUGH A SPATIOTEMPORAL HARMONIC-BALANCE TECHNIQUE

The characteristics of spatio-temporal periodic oscillations occurring in CNNs composed by a finite number of cells are investigated through a harmonic balance technique. It is shown that for an N-cell CNN desc ribed by the template [a(-1),a(0),a(1)], this technique leads to a set of 2N non-linear equations that can be reduced to N + 1 equations thr ough suitable algebraic manipulations. Then it is assumed that the amp litudes of the oscillations of the cells located in the middle of the network are approximately constant. Such an assumption, which is confi rmed by the simulation results, allows us to solve accurately the set of N + 1 equations by considering no more than six suitable non-linear equations, regardless of the number of cells. The method is useful fo r predicting all the main features of spatio-temporal periodic oscilla tions and yields results that are in good agreement with those observe d by the time simulation of the network. (C) 1997 by John Wiley & Sons , Ltd.