Finite-size effect in Kuramoto phase oscillators with higher-order interactions

TL;DR

This paper investigates how finite-size effects influence the synchronization transition in Kuramoto oscillators with higher-order interactions, revealing early transitions and new partially synchronized states not present in the thermodynamic limit.

Contribution

It demonstrates the impact of finite-size fluctuations on synchronization dynamics and identifies a novel partially synchronized state in two-population systems.

Findings

Finite-size fluctuations cause earlier synchronization transitions.

A new partially synchronized fixed point emerges due to finite-size effects.

Transition probabilities vary with system size and are numerically characterized.

Abstract

Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto phase oscillators with higher-order interactions, and observe that fluctuations inherent to finite-size systems drives the transition to the synchronized state occurring before the critical point in the thermodynamic limit. Using numerical methods, we plot the first exit time distribution of the magnitude of complex order parameter and obtain numerical transition probabilities across various system sizes. Further, we extend this study to a two-population oscillator system, and using velocity field of the associated order parameters, show the emergence of a new fixed point corresponding to a partially synchronized state arising due to the finite-size effect which is absent in the thermodynamics limit.