One- and two-dimensional wave fronts in diffusive systems with discrete sets of nonlinear sources

We study the dynamics of one-and two-dimensional diffusion systems with set s of discrete nonlinear sources. We show that wave fronts propagating in su ch systems are pinned if the diffusion constant is below a critical value w hich corresponds to a saddle-node bifurcation of the dynamics. In two dimen sions we find that the dissipation is enhanced and moving plain and circula r fronts are stable with respect to any perturbations. (C) 1999 Elsevier Sc ience B.V. All rights reserved.