One- and Two-Dimensional Wave Fronts in Diffusive Systems With Discrete Sets of Nonlinear Sources

The authors study the dynamics of on- and two-dimensional diffusion systems with sets of discrete nonlinear sources. They show that wave fronts propagating in such systems are pinned if the diffusion constant is below a critical value which corresponds to a saddle-node bifurcation of the dynamics. In two dimensions they find that the dissipation is enhanced and moving plain and circular fronts are stable with respect to any perturbations