Fluctuations and stability in front propagation

TL;DR

This paper investigates how stochastic fluctuations influence front propagation in reaction-diffusion systems, revealing that large fluctuations can reverse wave direction, contrasting with deterministic predictions.

Contribution

It provides an example demonstrating that fluctuations can alter the stability and direction of propagating fronts in reaction-diffusion models.

Findings

Fluctuations can reverse wave propagation direction.

Deterministic and stochastic effects differ at large fluctuations.

The spruce-budworm model illustrates fluctuation-driven stability changes.

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.