Eur. Phys. J. E (2015) 38: 10
https://doi.org/10.1140/epje/i2015-15010-y

Regular Article

Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves

¹ Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, D-10587, Berlin, Germany
² Department of Physics, Humboldt Universität zu Berlin, Robert-Koch-Platz 4, 10115 Berlin, Berlin, Germany

^* e-mail: fkneer@ni.tu-berlin.de

Received: 5 September 2014
Revised: 18 November 2014
Accepted: 21 January 2015
Published online: 25 February 2015

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.