Stochastic waves in a Brusselator model with nonlocal interaction

TL;DR

This paper demonstrates that intrinsic noise can generate spatio-temporal patterns like Turing patterns and travelling waves in a nonlocal Brusselator model, with analytical predictions validated by simulations.

Contribution

It introduces a system-size expansion approach to analyze stochastic quasi-waves in nonlocal reaction-diffusion systems, providing analytical tools for pattern prediction.

Findings

Intrinsic noise induces Turing patterns and travelling waves.

Analytical power spectra match simulation results.

Nonlocal models in other fields may exhibit similar stochastic patterns.

Abstract

We show that intrinsic noise can induce spatio-temporal phenomena such as Turing patterns and travelling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these quasi-waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the quasi-waves analytically, and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically-induced patterns.