# Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling

## TL;DR

This paper investigates how finite-sized populations of nonlinear coupled oscillators transition to synchrony, revealing that such transitions occur only in finite systems and vanish in the infinite limit, with established scaling laws.

## Contribution

It introduces a self-consistent approach and numerical simulations to show finite-size effects induce synchronization transitions in nonlinear oscillator ensembles, absent in the thermodynamic limit.

## Key findings

- Transitions to synchrony occur only in finite systems.
- Scaling relations link order parameter, coupling, and system size.
- Synchronization disappears as system size approaches infinity.

## Abstract

We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles, and disappears in the thermodynamic limit. For all considered setups, that include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.