A linear path toward synchronization: Anomalous scaling in a new class of exactly solvable Kuramoto models

TL;DR

This paper introduces a new class of exactly solvable Kuramoto models that exhibit anomalous logarithmic scaling near the critical point, expanding understanding of synchronization phenomena.

Contribution

It presents a linear reformulation of the Kuramoto model and analyzes a novel coupling scheme leading to exact solutions and unique scaling behavior.

Findings

Logarithmic scaling law near critical point

Exact solvability of the new oscillator class

Deviation from standard power-law behavior

Abstract

Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems (arXiv:0704.1166), we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We show that these systems have a logarithimic scaling law in the vicinity of the critical point, which may be seen as anomalous with respect to the usual power-law behavior exhibited by the standard Kuramoto model.