Fluctuation-driven Turing patterns

TL;DR

This paper demonstrates that intrinsic noise in diffusion models can generate quasi-patterns, eliminating the need for fine tuning or scale separation in Turing pattern formation, with implications for ecological systems.

Contribution

It introduces noise-driven quasi-patterns in Turing models, broadening the conditions under which spatial patterns can form without fine tuning.

Findings

Quasi-patterns form in generic parameter regions.

Noise induces pattern formation without scale separation.

Quasi-patterns are experimentally distinguishable from classical Turing patterns.

Abstract

Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ecological pattern formation, we show that the inclusion of intrinsic noise in Turing models leads to the formation of "quasi-patterns" that form in generic regions of parameter space and are experimentally distinguishable from standard Turing patterns. The existence of quasi-patterns removes the need for unphysical fine tuning or separation of scales in the application of Turing models to real systems.