  Chemical, physical and ecological systems passing through a saddle-node
bifurcation will, momentarily, find themselves balanced at a semi-stable steady
state. If perturbed by noise, such systems will escape from the zero-steady
state, with escape time sensitive to noise. When the model is extended to
include space, this leads to different points in space "escaping from zero" at
different times, and uniform initial conditions nucleate into sharp peaks
spread randomly across a nearly uniform background, a phenomena closely
resembling nucleation during phase transition. We use Large Deviation Theory to
determine burst shape and temporal scaling with respect to noise amplitude.
These results give a prototype for a particular form of patternless symmetry
breaking in the vicinity of a stability boundary, and demonstrates how
microscopic noise can lead to macroscopic effects in such a region.

Statistical Mechanics;Probability