Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes.
Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes.
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DOI：
10.1063/1.4914450
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发表时间：
2015-03
期刊：
影响因子：
2.9
通讯作者：
E. Siero;A. Doelman;M. Eppinga;J. Rademacher;Max Rietkerk;Koen Siteur
中科院分区：
文献类型：
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作者：
E. Siero;A. Doelman;M. Eppinga;J. Rademacher;Max Rietkerk;Koen Siteur
对于水分有限的干旱生态系统，水分分布和渗透起着至关重要的作用，已经建立了各种模型来解释植被格局。在斜坡地形上，植被排列成带状，随处可见。在本文中，我们考虑的出现，稳定性和分歧的二维条纹或带状图案在干旱生态系统模型。我们数值计算表明，植被带的弹性较大的陡坡计算的稳定区域（Busse气球）的条纹图案相对于1D和横向2D扰动。这是证实了数值模拟与缓慢降低的水输入参数。在这里，长波长条纹图案对于横向扰动是不稳定的，我们也通过埃文斯函数方法在平地上严格证明了这一点。此外，我们证明了一个“乡绅定理”的一类两个组件的反应，平流，扩散系统，包括我们的模型，显示在2D模式形成的发病是由于一维不稳定性的平流方向，这自然会导致条纹图案。
For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns.