title: Dynamics of reaction-diffusion systems in a subdiffusive regime.
abstract: In this paper, we examine the dynamics of reaction-diffusion systems with fractional time derivatives. It is shown that in these conditions diffusion is anomalous, in the sense that the mean-square displacement r2 approximately tgamma, where gamma<1, a situation known as subdiffusion. We study the conditions for the appearance of a diffusion-driven instability and show that the restrictive conditions for a Turing instability are relaxed. This implies that systems whose kinetics are not of the activator-inhibitor kind can have a Turing instability and a modulated final state. We demonstrate our results with numerical calculations in two dimensions using a generic Turing model.
authors.affiliation: Instituto de Fisica, Universidad Nacional Autónoma de México (UNAM), Apartado Postal 20-364 01000 México, D.F., Mexico.
authors.forename: D
authors.initials: D
authors.lastname: Hernández
authors.forename: C
authors.initials: C
authors.lastname: Varea
authors.forename: R A
authors.initials: RA
authors.lastname: Barrio