Fisher waves in reaction random walks

We study systems of particles that disperse via a persistent random walk and undergo branching-coalescence reactions in the activation-controlled regime. These reaction random walks represent a generalization of the Fisher reaction-diffusion equation. Activation control can be modelled in reaction random walks either implicitly, using direction-independent kinetics, or explicitly, using direction-dependent kinetics. We show that traveling waves exist in both cases and that the minimal wave speeds are smaller than for the classical Fisher equation. (C) 1999 Elsevier Science B.V. All rights reserved.