Coarse-grained description of general oscillator networks

TL;DR

This paper introduces a new systematic method for simplifying complex oscillator networks into coarse-grained models using eigenmodes, aiding analysis of their collective dynamics.

Contribution

The authors develop a novel coarse-graining approach based on eigenvalue problems and nonlinear transformations for oscillator networks described by phase equations.

Findings

Successfully applied to oscillator dynamics on a random graph.

Captured saddle-node bifurcation behavior.

Enabled derivation of closed-form coarse-grained equations.

Abstract

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.