From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators

TL;DR

This paper investigates the synchronization behavior of oscillator lattices under noise, revealing a transition to explosive desynchronization linked to KPZ surface growth theory and finite-time singularities.

Contribution

It connects KPZ surface growth theory to oscillator synchronization, identifying a dynamical transition and instability in 1D and 2D lattices with local coupling.

Findings

KPZ scaling observed in 1D lattices under certain conditions

A dynamical instability leads to explosive desynchronization in 1D and 2D

Finite-time singularity prevents KPZ scaling observation in 2D

Abstract

We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable Kuramoto-Sakaguchi model, with local couplings between oscillators. For smooth phase fields, the time evolution can initially be described by a surface growth model, the Kardar-Parisi-Zhang (KPZ) theory. We delineate the regime in which one can indeed observe the universal KPZ scaling in 1D lattices. For larger couplings, both in 1D and 2D, we observe a stochastic dynamical instability that is linked to an apparent finite-time singularity in a related KPZ lattice model. This has direct consequences for the frequency stability of coupled oscillator lattices, and it precludes the observation of non-Gaussian KPZ-scaling in 2D lattices.