We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is based on the eigenvalue problem of the linearized system around the phase-locked solution and a nonlinear transformation. We demonstrate our method by applying it to oscillator dynamics on a random graph, which exhibits a saddle-node bifurcation at the bifurcation point.
@article{arxiv.1311.0917,
title = {Coarse-grained description of general oscillator networks},
author = {Yuki Izumida and Hiroshi Kori},
journal= {arXiv preprint arXiv:1311.0917},
year = {2013}
}