A moment based approach to the dynamical solution of the Kuramoto model

TL;DR

This paper introduces a moment-based analytical method to exactly solve the dynamics of the Kuramoto model, enabling efficient numerical analysis and revealing an effective Hamiltonian governing the system.

Contribution

The authors develop a novel moment-based formalism that exactly closes the dynamical equations of the Kuramoto model, facilitating analysis and numerical investigation.

Findings

Exact closure of dynamical equations using moments

Identification of an effective Hamiltonian for the system

Numerical investigation free from finite size effects

Abstract

We examine the dynamics of the Kuramoto model with a new analytical approach. By defining an appropriate set of moments the dynamical equations can be exactly closed. We discuss some applications of the formalism like the existence of an effective Hamiltonian for the dynamics. We also show how this approach can be used to numerically investigate the dynamical behavior of the model without finite size effects.