克隆植物生长简化模型中的模式、局部结构和前沿
Patterns, localized structures and fronts in a reduced model of clonal plant growth
摘要：
克隆植物生长的简化模型制定，动机在地中海Posidonia oceanica草甸的空间结构的观察。两个层次的近似被认为是尺度相关的反馈项。两者都考虑到死亡率和克隆，或营养，生长以及竞争和促进，但第一个版本是非本地的空间，而第二个是本地的。在一维情况下的两个版本的模型的研究表明，这两种情况下表现出定性相似的行为（但定量差异），并描述了三个空间扩展的状态，裸土状态，人口状态，和模式状态之间的竞争，以及相关的空间局部化结构。后者有两种类型，孔在人口稠密的国家和植被斑块裸露的地面上，并组织在不同的蛇形分叉图。三个扩展状态之间的前线进行了研究，并确定推和拉前线之间的过渡。在一个空间维度的数值模拟被用来确定前速度和面对的边缘稳定性条件的预测拉锋。
英文摘要：
A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback terms. Both take into account mortality and clonal, or vegetative, growth as well as competition and facilitation, but the first version is nonlocal in space while the second is local. Study of the two versions of the model in the one-dimensional case reveals that both cases exhibit qualitatively similar behavior (but quantitative differences) and describe the competition between three spatially extended states, the bare soil state, the populated state, and a pattern state, and the associated spatially localized structures. The latter are of two types, holes in the populated state and vegetation patches on bare ground, and are organized within distinct snaking bifurcation diagrams. Fronts between the three extended states are studied and a transition between pushed and pulled fronts identified. Numerical simulations in one spatial dimension are used to determine front speeds and confront the predictions from the marginal stability condition for pulled fronts.
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