Knowledge Resource Center for Ecological Environment in Arid Area
DOI | 10.1137/120862648 |
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
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ISSN | 0036-1399 |
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 |
推荐引用方式 GB/T 7714 | 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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