Analysis of nonlinear oscillatory network dynamics via time-varying amplitude and phase variables

摘要

The goal of this manuscript is to propose a method for investigating the global dynamics of nonlinear oscillatory networks, with arbitrary couplings. The procedure is mainly based on the assumption that the dynamics of each oscillator is accurately described by a couple of variables, that is, the oscillator periodic orbits are represented through time-varying amplitude and phase variables. The proposed method allows one to derive a set of coupled nonlinear ordinary differential equations governing the time-varying amplitude and phase variables. By exploiting these nonlinear ordinary differential equations, the prediction of the total number of periodic oscillations and their bifurcations is more accurate and simpler with respect to the one given by the latest available methodologies. Furthermore, it is proved that this technique also works for weakly connected oscillatory networks. Finally, the method is applied to a chain of third-order oscillators (Chua's circuits) and the results are compared with those obtained via a numerical technique, based on the harmonic balance approach.