Phase model reduction and synchronization of nonlinear oscillators by a periodic force

Phase models represent the ideal framework to investigate the synchronization of a nonlinear oscillator by an external periodic force. While many researches focused the attention to their analysis, little work has been done about the reduction of a physical system to the corresponding phase model. In this paper we show how, resorting to the method of averaging, it is possible to obtain the phase model corresponding to a given set of state equations. As examples, we derive the phase equations and investigate the synchronization properties of two popular nonlinear oscillators.