Phase Model Reduction and Phase Locking of Coupled Nonlinear Oscillators

The synchronization of an oscillator with an external stimulus or between coupled elements is the subject of intense research in many areas of ap-plied 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 wealth of details and in a plethora of dif-ferent 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 investigate the possibility, at least within the context of analytical approx-imations, 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