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Chemical, physical and ecological systems passing through a saddle-nodebifurcation will, momentarily, find themselves balanced at a semi-stable steadystate. If perturbed by noise, such systems will escape from the zero-steadystate, with escape time sensitive to noise. When the model is extended toinclude space, this leads to different points in space "escaping from zero" atdifferent times, and uniform initial conditions nucleate into sharp peaksspread randomly across a nearly uniform background, a phenomena closelyresembling nucleation during phase transition. We use Large Deviation Theory todetermine burst shape and temporal scaling with respect to noise amplitude.These results give a prototype for a particular form of patternless symmetrybreaking in the vicinity of a stability boundary, and demonstrates howmicroscopic noise can lead to macroscopic effects in such a region.

Timing and Shape of Stochastic Autocatalytic Burst Formation