Turing Patterns in two dimensional reaction-diffusion system: effect of an electric field

TL;DR

This paper analyzes how an electric field influences Turing pattern formation in a two-dimensional reaction-diffusion system with charged species, providing an analytical stability criterion that accounts for diffusion and drift effects.

Contribution

It derives an analytical formula for stability in a charged species reaction-diffusion system under electric fields, extending previous numerical studies.

Findings

Analytical stability criterion incorporating electric field effects.

Electric field can induce or suppress Turing patterns.

Provides detailed predictions for pattern behavior under electric influence.

Abstract

We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift induced instability found by A.B.Rovinsky and M.Menzinger\cite{9}. This allows one to study the competition between diffusion and drift as was done numerically by Riaz et al. We show here that an analytic formula can be found on the basis of a linear stability analysis that incorporates all the effects that are known for the system and also allows for some detailed predictions.