On a nonlocal system for vegetation in drylands
On a nonlocal system for vegetation in drylands
复制标题
DOI：
10.1007/s00285-018-1215-0
复制
发表时间：
2018-02
影响因子：
1.9
通讯作者：
M. Alfaro;H. Izuhara;M. Mimura
中科院分区：
文献类型：
--
作者：
M. Alfaro;H. Izuhara;M. Mimura
提出了几个数学模型，以了解旱地出现的空间斑块状植被格局。在本文中，我们认为系统与非本地传播的植物（通过种子的再分配内核）提出的Pueyo等。（Oikos 117：1522-1532，2008）作为一个模型的植被在水有限的生态系统。它包括两个反应扩散方程的地表水和土壤水，结合一个积分微分方程的植物。对于这个系统，在适当的假设下，我们证明了适定性使用Schauder不动点定理。此外，我们认为从植被格局形成的观点的平稳问题，并显示过渡的植被格局时，参数值（降雨量，种子传播范围，种子发芽率）在系统中的变化。讨论了重分布核形状的影响。
Several mathematical models are proposed to understand spatial patchy vegetation patterns arising in drylands. In this paper, we consider the system with nonlocal dispersal of plants (through a redistribution kernel for seeds) proposed by Pueyo et al. (Oikos 117:1522–1532, 2008) as a model for vegetation in water-limited ecosystems. It consists in two reaction diffusion equations for surface water and soil water, combined with an integro-differential equation for plants. For this system, under suitable assumptions, we prove well-posedness using the Schauder fixed point theorem. In addition, we consider the stationary problem from the viewpoint of vegetated pattern formation, and show a transition of vegetation patterns when parameter values (rainfall, seed dispersal range, seed germination rate) in the system vary. The influence of the shape of the redistribution kernel is also discussed.