Analysis of periodic oscillations in finite-dimensional CNNs through a spatio–temporal harmonic balance technique
Marco Gilli · International Journal of Circuit Theory and Applications · 1997
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 described by the template [a-1, a0, a1], this technique leads to a set of 2N non-linear equations that can be reduced to N+1 equations through suitable algebraic manipulations. Then it is assumed that the amplitudes of the oscillations of the cells located in the middle of the network are approximately constant. Such an assumption, which is confirmed 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 for predicting all the main features of spatio–temporal periodic oscillations and yields results that are in good agreement with those observed by the time simulation of the network. © 1997 John Wiley & Sons, Ltd.