Noise synchronisation and stochastic bifurcations in lasers

TL;DR

This paper investigates how external white Gaussian noise induces synchronization and subsequent desynchronization in an ensemble of lasers, revealing stochastic bifurcations and unstable attractors through local analysis.

Contribution

It introduces a detailed analysis of noise-induced synchronization and stochastic bifurcations in laser systems, including the calculation of bifurcation loci and uncovering a square-root law.

Findings

Synchronization onset and loss due to noise strength

Identification of stochastic bifurcation to a strange attractor

Bifurcation locus in parameter space calculated

Abstract

This paper studies noise synchronisation in terms of random pullback attractors and their instabilities. We consider an ensemble of uncoupled lasers, each being a limit-cycle oscillator, which are driven by the same external white Gaussian noise. As the external-noise strength increases, there is an onset of synchronization and then subsequent loss of synchrony. Local analysis of the laser equations shows that synchronization becomes unstable via stochastic bifurcation to a random strange attractor. The locus of this bifurcation is calculated in the three-dimensional parameter space defined by the Hopf parameter, amount of amplitude-phase coupling or shear, and external-noise strength. The analysis uncovers a square-root law for this stochastic bifurcation.