Eur. Phys. J. B (2015) 88: 222
https://doi.org/10.1140/epjb/e2015-60269-0

Regular Article

Pattern formation for reactive species undergoing anisotropic diffusion

¹ Dipartimento di Fisica e Astronomia “G. Galilei”, University of Padova, Via Marzolo, 8, 35131 Padova, Italy
² Department of mathematics and Namur Center for Complex Systems – naXys, University of Namur, rempart de la Vierge 8, 5000 Namur, Belgium
³ Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC, Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy

^a e-mail: timoteo.carletti@unamur.be

Received: 3 April 2015
Received in final form: 6 June 2015
Published online: 9 September 2015

Abstract

Turing instabilities for a two species reaction-diffusion system is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive. Under this working hypothesis, the conditions for the onset of the instability are mathematically derived and numerically validated. Patterns which closely resemble those obtained in the classical context of isotropic diffusion, develop when the usual Turing condition is violated, along one of the two accessible directions of migration. Remarkably, the instability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched.