Limit Cycles and Bifurcations in Nonlinear Oscillatory Networks

The aim of this work is to study periodic oscillations and bifurcations in oscillatory networks with 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. It allows us to derive a set of ordinary differential equations governing the amplitude and phase dynamics. 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.