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

TL;DR

This paper investigates how advection influences the critical speed of traveling waves in reaction-diffusion systems, revealing that advection can induce stable wave propagation even in non-excitable regimes, supported by analytical and numerical results.

Contribution

It introduces a novel analysis of unstable slow waves' role in determining critical advection strength, extending previous models focused on stable fast waves.

Findings

Advection can induce stable wave propagation in non-excitable regimes.

An analytical expression for the advection-velocity relation of unstable slow waves is derived.

Numerical simulations confirm the theoretical predictions.

Abstract

The effect of advection on the critical minimal speed of traveling waves is studied. Previous theoretical studies estimated the 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, the critical advection strength is calculated taking into account the unstable slow wave solution. Thereby, theoretical results predict, that advection can induce stable wave propagation in the non-excitable parameter regime, if the advection strength exceeds a critical value. In addition, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. Predictions are confirmed numerically in a two-variable reaction-diffusion model.