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.
- Received 26 October 2009
DOI:
Authors & Affiliations
Tommaso Biancalani
- Dipartimento di Fisica, Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Florence, Italy
Duccio Fanelli
- Dipartimento di Energetica, Università degli Studi di Firenze, via S. Marta 3, 50139 Florence, Italy and INFN, Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Florence, Italy
Francesca Di Patti
- Dipartimento di Fisica “Galileo Galilei,” Università degli Studi di Padova, via F. Marzolo 8, 35131 Padova, Italy