Density of instantaneous frequencies in the Kuramoto-Sakaguchi model

TL;DR

This paper derives a detailed formula for the distribution of instantaneous frequencies in the Kuramoto-Sakaguchi model, providing insights into the stationary states of coupled oscillators.

Contribution

It presents a new analytical formula for the stationary distribution of frequencies in the Kuramoto-Sakaguchi model, supported by numerical validation.

Findings

The formula accurately describes stationary frequency distributions.

Numerical simulations confirm the theoretical predictions.

The work enhances understanding of collective states in coupled oscillators.

Abstract

We obtain a formula for the statistical distribution of instantaneous frequencies in the Kuramoto-Sakaguchi model. This work is based on the Kuramoto-Sakaguchi's theory of globally coupled phase oscillators, which we review in full detail by discussing its assumptions and showing all steps behind the derivation of its main results. Our formula is a stationary probability density function with a complex mathematical structure, is consistent with numerical simulations and gives a description of the stationary collective states of the Kuramoto-Sakaguchi model.