Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit

TL;DR

This paper introduces a new model reduction method for finite networks of globally coupled oscillators that accurately captures their collective dynamics and bifurcation structure, bridging finite and infinite network analyses.

Contribution

It proposes a novel ansatz based on the collective coordinate approach that improves finite network modeling and reproduces thermodynamic limit behavior.

Findings

Accurately reproduces collective dynamics of finite oscillator networks.

Replicates bifurcation structure in the thermodynamic limit.

Captures critical slowing down near bifurcations.

Abstract

Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here we propose a new ansatz, based on the collective coordinate approach, that reproduces the collective dynamics of the Kuramoto model for finite networks to high accuracy, yields the same bifurcation structure in the thermodynamic limit of infinitely many oscillators as previous approaches, and additionally captures the dynamics of the order parameter in the thermodynamic limit, including critical slowing down that results from a cascade of saddle-node bifurcations.