The Kuramoto model with distributed shear

TL;DR

This paper introduces a solvable extension of the Kuramoto model incorporating distributed shear and natural frequencies with dependence, revealing how their interaction influences synchronization and phase transitions.

Contribution

It presents a new generalized Kuramoto model with dependent distributions of shear and frequencies, providing analytical solutions and stability criteria.

Findings

Dependence between shear and frequencies significantly affects synchronization.

Analytical results for specific joint distributions using Ott-Antonsen ansatz.

Derived stability boundaries for incoherent states.

Abstract

We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence.