Stochastic Turing patterns in the Brusselator model

2009/10/31 by Tommaso Biancalani, Duccio Fanelli, Francesca Di Patti · 4 citations
Computer Science · Environmental Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Brusselator #Computer science #Ecosystem dynamics and resilience #Field (mathematics) #Heuristic #Instability #Mathematical optimization #Mathematics #Mean field theory #Mechanics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Pure mathematics #Stability (learning theory) #Statistical physics #Turing #cond-mat.stat-mech #nlin.AO

paper · pdf · doi:10.1103/physreve.81.046215

modified version submitted to Phys Rev. E. 5. 3 Figures (5 panels) added

arxiv created 2010/02/04 · openalex publication_date 2010/04/27 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• The chemical basis of morphogenesis
• Predator-Prey Cycles from Resonant Amplification of Demographic Stochasticity
• Stochastic Processes in Physics and Chemistry

Cited by

• Oscillations and Spatial Patterns in Large-Scale Stochastic Gene Regulatory Networks
• Noise seeded oscillators: on the role of demographic fluctuations in a multi-populations model
• Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction
• Evolution of specialized microbial cooperation in dynamic fluids

Related

• Stochastic Turing Patterns for systems with one diffusing species
• Stochastic Turing patterns: analysis of compartment-based approaches
• Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory
• Stochastic Turing pattern formation in a model with active and passive transport
• Turing patterns on a two-component isotropic growing system. Part 3: Time dependent conditions and linear growth