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Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves
Citation key Kneer2015
Author Kneer, F. and Obermayer, K. and Dahlem, M. A.
Year 2015
ISSN 1292-8941
DOI 10.1140/epje/i2015-15010-y
Journal The European Physical Journal E
Volume 38
Number 10
Publisher Springer Berlin Heidelberg
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.
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