Stochastic Turing Patterns on a Network

TL;DR

This paper investigates stochastic Turing patterns on networks using the Brusselator model, revealing how noise induces pattern formation outside classical deterministic conditions, explained through analytical and simulation methods.

Contribution

It demonstrates stochastic Turing instability on networks and provides an analytical explanation linking finite size effects to pattern emergence.

Findings

Stochastic Turing patterns form outside classical parameter regions.

Finite size effects are crucial for pattern formation.

Analytical and simulation results agree on the mechanism.

Abstract

The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically, and eventually traced back to the finite size corrections stemming from the inherent graininess of the scrutinized medium.