Sufficient conditions for wave instability in three-component reaction-diffusion systems

TL;DR

This paper derives criteria based on the Jacobian matrix to predict wave instabilities in three-component reaction-diffusion systems, including cases where one species does not diffuse, aiding the search for such instabilities.

Contribution

It introduces new sufficient conditions for wave instability in three-component systems, applicable even when one species is non-diffusive.

Findings

Wave instability can occur with increased mobility of a species.

Instability criteria are expressed via the Jacobian matrix.

Wave instability can happen even if one species does not diffuse.

Abstract

Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to determine whether the wave instability can be observed as the mobility of one of the species is gradually increased. It is found that the instability can also occur if one of the three species does not diffuse. Our results provide a useful criterion for searching wave instabilities in reaction-diffusion systems of various origins.