Eur. Phys. J. B (2013) 86: 142
https://doi.org/10.1140/epjb/e2013-30649-7

Regular Article

Turing instabilities in reaction-diffusion systems with cross diffusion

¹ Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
² INFN, Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
³ Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, via S. Marta 3, 50139 Florence, Italy

^a e-mail: duccio.fanelli@gmail.com

Received: 19 July 2012
Received in final form: 13 December 2012
Published online: 10 April 2013

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.