Multispecies reaction diffusion models and the Turing instability revisited
Abstract
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share the same spatial reservoir and experience a degree of mutual interference due to the competition for the available resources. Turing instability can set in for all ratios of the main diffusivities, also when the (isolated) activator diffuses faster then the (isolated) inhibitor. This conclusion, at odd with the conventional vision, is here exemplified for the Brusselator model and ultimately stems from having assumed a generalized model of multispecies diffusion, fully anchored to first principles, which also holds under crowded conditions.
Cite
@article{arxiv.1112.0870,
title = {Multispecies reaction diffusion models and the Turing instability revisited},
author = {Duccio Fanelli and Claudia Cianci and Francesca Di Patti},
journal= {arXiv preprint arXiv:1112.0870},
year = {2012}
}
Comments
Submitted to the Journal of Theoretical Biology. The novel version of the paper contains a simple explaination of the physical process inspected as well as a new set of stochastic simulations. We make also contact with the literature devoted to Quasi Stationary States in Long Range systems