Effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems

TL;DR

This paper investigates how randomness and anisotropy influence Turing pattern formation in reaction-diffusion systems, demonstrating the robustness of the Turing mechanism under various stochastic and directional conditions.

Contribution

It introduces a comprehensive analysis of the effects of lattice randomness and anisotropic diffusion on Turing patterns using the Gierer-Meinhardt model.

Findings

Turing patterns are robust despite lattice randomness.

Anisotropic and random diffusion coefficients still support pattern formation.

Abstract

We study the effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of pattern formation is considered. The cases we study are: (i)randomness in the underlying lattice structure, (ii)the case in which there is a probablity p that at a lattice site both reaction and diffusion occur, otherwise there is only diffusion and lastly, the effect of (iii) anisotropic and (iv) random diffusion coefficients on the formation of Turing patterns. The general conclusion is that the Turing mechanism of pattern formation is fairly robust in the presence of randomness and anisotropy.