Stochastic Turing patterns in the Brusselator model

TL;DR

This paper introduces a stochastic version of the Brusselator model, demonstrating that stochastic fluctuations can induce Turing patterns over a broader parameter range than classical deterministic models.

Contribution

It develops a stochastic Brusselator model and shows that noise can promote pattern formation beyond traditional Turing conditions.

Findings

Stochastic fluctuations induce spatially ordered solutions.

The stochastic Turing region is wider than the deterministic one.

Cross diffusive terms influence the Turing instability.

Abstract

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross diffusive terms, often neglected in the heuristic derivation of reaction diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.