Self-organisation of random oscillators with L\'evy stable distributions

TL;DR

This paper explores how Le9vy stable distributions influence the self-organization and synchronization of stochastic oscillators, revealing that Le9vy noise enhances synchronization and that rare extreme events can dominate long-term dynamics.

Contribution

It introduces the concept that Le9vy stable processes can significantly improve oscillator synchronization and examines the effects of extreme outliers and external noise on system behavior.

Findings

Le9vy stable processes lead to more efficient synchronization than Gaussian noise.

Rare extreme events can dominate the long-term behavior of coupled oscillators.

External Le9vy noise impacts synchronization properties.

Abstract

A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by L\'evy stable processes is significantly more efficient than that by oscillators with Gaussian statistics. The impact of outlier events from the tail of the distribution function was examined by artificially introducing a few additional oscillators with very strong coupling strengths and it is found that remarkably even one such rare and extreme event may govern the long term behaviour of the coupled system. In addition to the multiplicative noise component, we have investigated the impact of an external additive L\'evy distributed noise component on the synchronisation properties of the oscillators.