# Noise-induced stabilization of collective dynamics

## TL;DR

This paper demonstrates that small additive noise can unexpectedly stabilize unstable collective oscillations in coupled oscillator systems, revealing noise-induced bifurcations and partial synchrony.

## Contribution

It introduces a semi-analytical approach to explain how small noise stabilizes unstable regimes in globally coupled oscillators, supported by numerical and stability analyses.

## Key findings

- Small white noise stabilizes unstable collective oscillations.
- Two distinct noise-induced bifurcations lead to partial synchrony.
- The macroscopic Fokker-Planck approach confirms the numerical results.

## Abstract

We illustrate a counter-intuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show numerically and semi-analytically that a very small white noise is able to stabilize an otherwise linearly unstable collective periodic regime. Microscopic simulations reveal two noise-induced bifurcations of different nature towards self-consistent partial synchrony. We develop a macroscopic treatment solving the corresponding nonlinear Fokker-Planck equation by means of a perturbative approach. The associated linear stability analysis confirms the results anticipated by the numerics. We also argue about the generality of the phenomenon.