PHASE MODEL REDUCTION AND PHASE LOCKING OF COUPLED NONLINEAR OSCILLATORS

Abstract

The synchronization of an oscillator with an external stimulus or between coupled elements is the subject of intense research in many areas of applied sciences. The most successful approach is based on phase modeling, founded on the idea to represent each oscillator by a phase variable. Phase models have been analyzed with a wealth of details and in a plethora of different variants, but little research has been done in view of the reduction of a physical system to the corresponding phase model. In this paper we investigate the possibility, at least within the context of analytical approximations, to obtain the phase model corresponding to a given nonlinear system. Both periodically driven and coupled oscillators are considered, and examples based on Stuart–Landau and van der Pol systems are given.