Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. V: The transition from patterns to desert
type: Item
instance of: scholarly article
zbMATH Open document ID: 1320.92078
DOI: 10.1137/120899510
published in: SIAM Journal on Applied Mathematics
publication date: 2013-11-14T00:00:00Z
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35M10
zbMATH DE Number: 6227169
zbMATH Keywords: pattern formation
zbMATH Keywords: arid landscapes
zbMATH Keywords: reaction-diffusion-advection
zbMATH Keywords: wavetrain
zbMATH Keywords: tiger bush
zbMATH Keywords: desertification
author: Jonathan A. Sherratt
MaRDI profile type: Publication
OpenAlex ID: W2046181545
title: Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. V: The transition from patterns to desert
review text: In this paper, a system of reaction-diffusion-advection equations involving the plant density and water density is considered. A very large dimensionless parameter (called the slope gradient) is studied, that reflects the relative rates of water flow downhill and plant dispersal. The author's concern is the existence and form of periodic travelling waves of the Klausmeier model, to leading order as the slope gradient tends to infinity, provided that the migration speed scales with the slope gradient in given ways. A~detailed numerical study of the existence and stability of periodic traveling waves is done via numerical procedures. The author shows via numerical simulations that a decrease in rainfall through the minimum level for patterns causes a transition to full-blown desert that cannot be reversed by increasing the rainfall again. The author includes a summary of the work done in his previous four papers on the Klausmeier model, as this is the last one of the series.NEWLINENEWLINEFor Part IV see [the author, ibid. 73, No. 1, 330--350 (2013; Zbl 1321.92083)].
reviewed by: Mariano Rodríguez Ricard
description: scientific article; zbMATH DE number 6227169