DYNAMICS OF PATCHY VEGETATION PATTERNS IN THE TWO-DIMENSIONAL GENERALIZED KLAUSMEIER MODEL

被引:1
作者
Wong, Tony [1 ]
Ward, Michael J. [2 ]
机构
[1] Brown Univ, Inst Computat & Expt Res Math, Providence, RI 02903 USA
[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2022年 / 15卷 / 09期
基金
加拿大自然科学与工程研究理事会;
关键词
Pattern formation; localized patterns; spatial ecology; singular perturbation theory; Green's function; bifurcation studies; BANDED VEGETATION; SPOT PATTERNS; SLOW PASSAGE; BIFURCATION; TRANSITION; STABILITY; DELAY;
D O I
10.3934/dcdss.2022043
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the dynamical and steady-state behavior of self-organized spatially localized patches or "spots" of vegetation for the Klausmeier reaction-diffusion (RD) system of spatial ecology that models the interaction between surface water and vegetation biomass on a 2-D spatial landscape with a spatially uniform terrain slope gradient. In this context, we develop and implement a hybrid asymptotic-numerical theory to analyze the existence, linear stability, and slow dynamics of multi-spot quasi-equilibrium spot patterns for the Klausmeier model in the singularly perturbed limit where the biomass diffusivity is much smaller than that of the water resource. From the resulting differential-algebraic (DAE) system of ODEs for the spot locations, one primary focus is to analyze how the constant slope gradient influences the steady-state spot configuration. Our second primary focus is to examine bifurcations in quasi-equilibrium multi-spot patterns that are triggered by a slowly varying time-dependent rainfall rate. Many full numerical simulations of the Klausmeier RD system are performed both to illustrate the effect of the terrain slope and rainfall rate on localized spot patterns, as well as to validate the predictions from our hybrid asymptotic-numerical theory.
引用
收藏
页码:2747 / 2793
页数:47
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