Fluctuations and stability in front propagation

Abstract

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small fluctuations (usually, large populations). However, for larger fluctuations propagation can be affected. We give an example, based on the classic spruce-budworm model, where the direction of wave propagation, i.e., the relative stability of two phases, can be reversed by fluctuations.

5 pages, 5 figures

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• Velocity fluctuations of stochastic reaction fronts propagating into an unstable state: strongly pushed fronts
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• Front propagation and effect of memory in stochastic desertification models with an absorbing state