# Network desynchronization by non-Gaussian fluctuations

## TL;DR

This paper develops a general theory for how non-Gaussian noise causes desynchronization in oscillator networks, revealing how noise statistics influence the rate and providing a simplified modeling approach.

## Contribution

It introduces a novel theoretical framework for analyzing network desynchronization under non-Gaussian fluctuations, including a reduction technique for complex networks.

## Key findings

- Higher moments of noise affect desynchronization rates exponentially.
- The theory predicts when noise accelerates or decelerates desynchronization.
- A reduction method simplifies network analysis to a single oscillator in some cases.

## Abstract

Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including electric power networks with renewable energy sources. Such non-Gaussian fluctuations can result in rare network desynchronization. Here we build a general theory for inertial oscillator network desynchronization by non-Gaussian noise. We compute the rate of desynchronization and show that higher-moments of noise enter at specific powers of coupling: either speeding up or slowing down the rate exponentially depending on how noise statistics match the statistics of a network's slowest mode. Finally, we use our theory to introduce a technique that drastically reduces the effective description of network desynchronization. Most interestingly, when instability is associated with a single edge, the reduction is to one stochastic oscillator.