Finite size effect in Kuramoto oscillators with inertia on simplicial complex

TL;DR

This paper studies how finite system size influences synchronization in Kuramoto oscillators with inertia on simplicial complexes, revealing finite-size driven transitions and the impact of inertia on critical coupling.

Contribution

It uncovers the finite-size effects on synchronization, identifies the transition origin, and quantifies how inertia shifts critical coupling in the Kuramoto model with triadic interactions.

Findings

Finite size induces synchronization at finite coupling, contrary to thermodynamic predictions.

A power-law relates network size to critical coupling for the transition.

Inertia increases the critical coupling, opposing finite-size effects.

Abstract

We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a synchronized state at finite coupling, which contrasts with the analytical predictions {in thermodynamic limit} made for the same system. Building on the analytical calculations performed at the thermodynamic limit, we identify the origin of the synchronization transition that arises because of the finite size. We discover a power-law relationship between the network size and the critical coupling at which the first-order transition to synchronization occurs. Additionally, as inertia increases, there is a significant shift in the critical coupling toward higher values, indicating that inertia counteracts the effects caused by finite size.