Limit Cycles and Bifurcations in Cellular Nonlinear Networks

The aim of this work is to study periodic oscillations and bifurcations in cellular nonlinear networks composed by oscillatory cells and connected through arbitrary couplings. In order to characterize each oscillator by using amplitude and phase variables, a method based on a generalized version of the describing function technique is proposed. Furthermore, by exploiting the method of multiple scales a set of ordinary differential equations governing the amplitude and phase dynamics is derived. The results also permit to study accurately weakly connected oscillatory networks. Finally, the method is compared to a spectral technique, based on the harmonic balance approach, by considering a chain of Chua´s circuits.