title: Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes.
abstract: For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns.
authors.affiliation: Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
authors.forename: E
authors.initials: E
authors.lastname: Siero
authors.affiliation: Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
authors.forename: A
authors.initials: A
authors.lastname: Doelman
authors.affiliation: Department of Environmental Sciences, Copernicus Institute, Faculty of Geosciences, Utrecht University, P.O. Box 80115, 3508 TC, Utrecht, The Netherlands.
authors.forename: M B
authors.initials: MB
authors.lastname: Eppinga
authors.affiliation: Fachbereich Mathematik, Universität Bremen, Postfach 33 04 40, 28359 Bremen, Germany.
authors.forename: J D M
authors.initials: JD
authors.lastname: Rademacher
authors.affiliation: Department of Environmental Sciences, Copernicus Institute, Faculty of Geosciences, Utrecht University, P.O. Box 80115, 3508 TC, Utrecht, The Netherlands.
authors.forename: M
authors.initials: M
authors.lastname: Rietkerk
authors.affiliation: Department of Environmental Sciences, Copernicus Institute, Faculty of Geosciences, Utrecht University, P.O. Box 80115, 3508 TC, Utrecht, The Netherlands.
authors.forename: K
authors.initials: K
authors.lastname: Siteur
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D017753:Ecosystem; D008954:Models, Biological; D017711:Nonlinear Dynamics; D063245:Plant Development / Q000502:physiology*; D014867:Water / Q000378:metabolism*
chemical_list: D014867:Water