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.Comment: 14 pages, 10 figure
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