Phase Description of Entrainment

By studying step by step cases (a)-(c), arranged in order of increasing complexity below, one may realize how Method I is suited for treating various synchronization phenomena. Before going into specific arguments, however, let us generalize the class of the perturbation ep in (3.2.2) to include time dependence  

Up to this stage, the generalization is trivial. When one averages with respect to rapidly oscillating processes, however, one must be very careful, and this point turns out to be crucial to the phase description of synchronization. 

---