Fisher waves in reaction random walks

We study systems of particles that disperse via a persistent random walk an d undergo branching-coalescence reactions in the activation-controlled regi me. These reaction random walks represent a generalization of the Fisher re action-diffusion equation. Activation control can be modelled in reaction r andom walks either implicitly, using direction-independent kinetics, or exp licitly, using direction-dependent kinetics. We show that traveling waves e xist in both cases and that the minimal wave speeds are smaller than for th e classical Fisher equation. (C) 1999 Elsevier Science B.V. All rights rese rved.