Kuramoto dynamics in Hamiltonian systems

TL;DR

This paper demonstrates how Kuramoto-like synchronization dynamics can emerge within a classical Hamiltonian system, establishing a link between dissipative and conservative collective behaviors.

Contribution

It introduces a Hamiltonian system that exactly reproduces Kuramoto dynamics on invariant manifolds, revealing the transition to synchronization through Hamiltonian instability.

Findings

Kuramoto dynamics can be embedded in Hamiltonian systems.

Synchronization transition corresponds to instability in Hamiltonian action dynamics.

Links dissipative synchronization phenomena with conservative Hamiltonian frameworks.

Abstract

The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony. Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that the synchronization transition on a Kuramoto manifold emerges where the transverse Hamiltonian action dynamics becomes unstable. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.