title: Effects of cross diffusion on Turing bifurcations in two-species reaction-transport systems.
abstract: We study the Turing bifurcation in general two-species reaction-transport systems, where particle dispersal is governed by diffusion, including cross diffusion. By performing a linear stability analysis, we find conditions for the Turing instability and compare the results with the standard Turing conditions. We apply our results to two model systems, the Lengyel-Epstein model and the Brusselator, and find strong effects of cross diffusion on the Turing bifurcation.
authors.affiliation: Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.
authors.forename: Niraj
authors.initials: N
authors.lastname: Kumar
authors.forename: Werner
authors.initials: W
authors.lastname: Horsthemke
mesh_terms: D004058:Diffusion; D007700:Kinetics; D016014:Linear Models; D008956:Models, Chemical