Renormalization Group Approach to Oscillator Synchronization

TL;DR

This paper introduces a renormalization group method to analyze synchronization clusters in disordered one-dimensional chains of coupled phase oscillators, providing insights into cluster statistics and length scales.

Contribution

The paper presents a novel renormalization group approach tailored for disordered oscillator chains, enabling detailed analysis of synchronization clusters and their statistical properties.

Findings

Good agreement between RG results and numerical simulations.

Cluster size and frequency distributions depend on Lorentzian parameters.

Characteristic cluster length varies with distribution parameters.

Abstract

We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling strengths. The results are compared with numerical simulations of the chain dynamics and good agreement in several characteristics is found. We apply the renormalization group and simulations to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies, as well as the dependence of the characteristic cluster length upon parameters of these Lorentzian distributions.