A phase model approach for synchronization analysis of coupled nonlinear oscillators

Networks of coupled nonlinear oscillators are popular mathematical models in many areas of applied sciences. The most successful approach for their analysis is based on phase modeling, founded on the idea to represent each oscillator by a phase variable. Phase models have been analyzed with wealth of details and in a plethora of different variants, but little research has been made in view of the reduction of a physical system to the corresponding phase model. In this paper we propose a technique to obtain the phase model corresponding to a given network. Examples based on Stuart-Landau and van der Pol oscillators are presented.