title: Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves.
abstract: The effect of advection on the propagation and in particular on the critical minimal speed of traveling waves in a reaction-diffusion model is studied. Previous theoretical studies estimated this effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. In addition, the critical advection strength is calculated taking into account the unstable slow wave solution. We also analyze a two-variable reaction-diffusion-advection model numerically in a wide parameter range. Due to the new control parameter (advection) we can find stable wave propagation in the otherwise non-excitable parameter regime, if the advection strength exceeds a critical value. Comparing theoretical predictions to numerical results, we find that they are in good agreement. Theory provides an explanation for the observed behaviour.
authors.affiliation: Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, D-10587, Berlin, Germany, fkneer@ni.tu-berlin.de.
authors.forename: Frederike
authors.initials: F
authors.lastname: Kneer
authors.forename: Klaus
authors.initials: K
authors.lastname: Obermayer
authors.forename: Markus A
authors.initials: MA
authors.lastname: Dahlem
mesh_terms: D004058:Diffusion; D057446:Hydrodynamics; D008956:Models, Chemical; D010507:Periodicity