title: Stochastic Turing patterns in the Brusselator model.
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.
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Firenze, via G Sansone 1, 50019 Sesto Fiorentino, Florence, Italy.
authors.forename: Tommaso
authors.initials: T
authors.lastname: Biancalani
authors.forename: Duccio
authors.initials: D
authors.lastname: Fanelli
authors.forename: Francesca
authors.initials: F
authors.lastname: Di Patti