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Stochastic Turing patterns in the Brusselator model.

Tommaso Biancalani1, Duccio Fanelli, Francesca Di Patti

  • 1Dipartimento di Fisica, Università degli Studi di Firenze, via G Sansone 1, 50019 Sesto Fiorentino, Florence, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a stochastic Brusselator model, revealing that random fluctuations can create Turing patterns. This self-organization occurs over a broader parameter range than previously thought.

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Area of Science:

  • Chemical kinetics
  • Non-equilibrium thermodynamics
  • Pattern formation

Background:

  • The Brusselator model is a classic reaction-diffusion system used to study pattern formation.
  • Conventional analysis often neglects cross-diffusion and stochastic effects.

Purpose of the Study:

  • To investigate a stochastic version of the Brusselator model.
  • To analyze the emergence of Turing patterns under stochastic conditions.
  • To compare stochastic self-organization with mean-field predictions.

Main Methods:

  • System size expansion of the stochastic Brusselator model.
  • Derivation of mean-field equations.
  • Analysis of Turing instability, including cross-diffusive terms.

Main Results:

  • Mean-field equations predict Turing patterns in a specific parameter region.
  • Stochastic fluctuations induce spatially ordered solutions (Turing patterns).
  • The parameter region for stochastic self-organization is wider than predicted by the conventional Turing approach.

Conclusions:

  • Stochasticity can drive pattern formation in reaction-diffusion systems.
  • Cross-diffusive terms play a crucial role in Turing instability.
  • The conditions for spatial self-organization may be less restrictive than traditionally assumed.