EXTERNAL NOISE AND FRONT PROPAGATION IN REACTION-TRANSPORT SYSTEMS WITH INERTIA: THE MEAN SPEED OF FISHER WAVES

Abstract

We review the effect of spatiotemporal noise, white in time and colored in space, on front propagation in systems of reacting and dispersing particles, where the particle motion displays inertia or persistence. We discuss the three main approaches that have been developed to describe transport with inertia, namely hyperbolic reaction-diffusion equations, reaction-Cattaneo systems or reaction-telegraph equations, and reaction random walks. We focus on the mean speed of Fisher waves in these systems and study in particular reaction random walks, which are the most natural generalization of reaction-diffusion equations. Hyperbolic reaction-diffusion equations account for inertia in the transport process in an ad hoc way, whereas the other reaction-transport systems have a proper macroscopic or microscopic foundation. For the former, external noise affects neither the mean wave speed nor the region in parameter space for which Fisher waves exist. For the latter, external noise increases the mean wave speed of Fisher waves and decreases the upper limit for the characteristic time of the transport process, below which propagating fronts exist.