Front propagation dynamics: Qualitative differences revealed by very high intensity fluctuations

Abstract

This paper presents a detailed analysis of the effect of a large external noise on the propagation of a front between two stable steady states. Noise affects one of the steady states or the thresholds. Significantdifferences with respect to the case of small noise intensity are carefully studied using a Langevin approach. The average effect of noise is modeled by means of an additional nonlinear term that enables an analysis of short-time and long-time behaviors. Nontrivial behaviors are numerically observed and analytically discussed: (i) Two symmetry breakings of the fluctuation-free stable states are observed and (ii) two fronts propagating in opposite directions are simultaneously observed and the propagation direction may be exchanged by changing the diffusion coefficient.