Arid
DOI10.1137/120862648
PATTERN SOLUTIONS OF THE KLAUSMEIER MODEL FOR BANDED VEGETATION IN SEMIARID ENVIRONMENTS IV: SLOWLY MOVING PATTERNS AND THEIR STABILITY
Sherratt, Jonathan A.1,2
通讯作者Sherratt, Jonathan A.
来源期刊SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN0036-1399
出版年2013
卷号73期号:1页码:330-350
英文摘要

Banded vegetation is a characteristic feature of semiarid environments, comprising stripes of vegetation running parallel to the contours on hillsides, separated by stripes of bare ground. Mathematical modelling plays an important role in the study of this phenomenon, and the Klausmeier model is one of the oldest and most established, consisting of coupled reaction-diffusion-advection equations for plant biomass and water density. In this model the dimensionless parameter corresponding to slope gradient is much larger than the other parameters, and this paper is part of a series investigating the asymptotic form of pattern solutions for large values of the slope parameter. The pattern solutions move uphill with a constant speed, c say, and the focus of this paper is c = O(1). I begin by deriving the leading order form of the patterns, and the region of parameter space in which they occur, for c = o(1). Using this, I show that all patterns with c = o(1) are unstable as model solutions for sufficiently large values of the slope parameter. I then consider patterns with c = O-s(1), showing that this region of parameter space contains both stable and unstable low amplitude patterns. I conclude by discussing the ecological implications of my results.


英文关键词pattern formation reaction diffusion advection stability perturbation theory arid landscapes Lame’s equation Weierstrass elliptic function
类型Article
语种英语
国家Scotland
收录类别SCI-E
WOS记录号WOS:000315581400016
WOS关键词SOUTH-WEST NIGER ; TIGER BUSH ; SELF-ORGANIZATION ; DYNAMICS ; WAVE ; LANDSCAPES ; ECOSYSTEMS ; ABSOLUTE ; SOIL ; CONTINUATION
WOS类目Mathematics, Applied
WOS研究方向Mathematics
来源机构Arizona State University
资源类型期刊论文
条目标识符http://119.78.100.177/qdio/handle/2XILL650/179937
作者单位1.Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland;
2.Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland
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Sherratt, Jonathan A.. PATTERN SOLUTIONS OF THE KLAUSMEIER MODEL FOR BANDED VEGETATION IN SEMIARID ENVIRONMENTS IV: SLOWLY MOVING PATTERNS AND THEIR STABILITY[J]. Arizona State University,2013,73(1):330-350.
APA Sherratt, Jonathan A..(2013).PATTERN SOLUTIONS OF THE KLAUSMEIER MODEL FOR BANDED VEGETATION IN SEMIARID ENVIRONMENTS IV: SLOWLY MOVING PATTERNS AND THEIR STABILITY.SIAM JOURNAL ON APPLIED MATHEMATICS,73(1),330-350.
MLA Sherratt, Jonathan A.."PATTERN SOLUTIONS OF THE KLAUSMEIER MODEL FOR BANDED VEGETATION IN SEMIARID ENVIRONMENTS IV: SLOWLY MOVING PATTERNS AND THEIR STABILITY".SIAM JOURNAL ON APPLIED MATHEMATICS 73.1(2013):330-350.
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