Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model
type: Item
instance of: scholarly article
title: Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model
zbMATH Open document ID: 1270.35093
author: Sjors van der Stelt
author: Arjen Doelman
author: Geertje Hek
author: Jens D. M. Rademacher
published in: Journal of Nonlinear Science
publication date: 2013-03-11T00:00:00Z
review text: The paper addresses bifurcations and pattern formation in the Klausmeier system, which is the basic model for the ecological dynamics of semi-arid areas. It includes two equations of the reaction-diffusion type, one for the density of water, and the other for the biomass density. In the present work, the water equation is supplemented by a nonlinear diffusion term, which accounts for subterranean propagation of water. The pattern formation through Turing and Turing-Hopf bifurcations in this system is studied, and an effective complex Ginzburg-Landau equation is derived for this case. It is demonstrated that bifurcations are of the supercritical type. In the second part of the paper, a full Busse balloon, i.e., a full stability region for patterns with nonsmall amplitudes, is obtained in a numerical form. It is concluded that the desertification may be cause by various factors represented in the model by respective coefficients.
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 35B36
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35Q56
zbMATH DE Number: 6143188
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: Busse balloon
zbMATH Keywords: Turing-Hopf bifurcations
zbMATH Keywords: supercritical type
describes a project that uses: AUTO
describes a project that uses: AUTO-07P
MaRDI profile type: Publication
full work available at URL: s00332-012-9139-0
OpenAlex ID: W2155145973
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DOI: 10.1007/S00332-012-9139-0
description: scientific article; zbMATH DE number 6143188