Multispecies reaction diffusion models and the Turing instability revisited

TL;DR

This paper revisits the Turing instability in multispecies reaction-diffusion models derived from microscopic principles, showing it can occur under broader conditions than traditionally thought, including when the activator diffuses faster than the inhibitor.

Contribution

It introduces a generalized multispecies diffusion model based on first principles, extending the understanding of Turing instability beyond classical assumptions.

Findings

Turing instability can occur for all diffusivity ratios.

The model applies under crowded conditions.

Revises the conventional view of diffusion roles in pattern formation.

Abstract

The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share the same spatial reservoir and experience a degree of mutual interference due to the competition for the available resources. Turing instability can set in for all ratios of the main diffusivities, also when the (isolated) activator diffuses faster then the (isolated) inhibitor. This conclusion, at odd with the conventional vision, is here exemplified for the Brusselator model and ultimately stems from having assumed a generalized model of multispecies diffusion, fully anchored to first principles, which also holds under crowded conditions.