具有密度依赖运动和两种相互作用尺度的种群的斑图形成
Pattern Formation in Populations with Density-Dependent Movement and Two Interaction Scales
摘要：
我们研究了由相互作用的粒子系统形成的空间格局，其中任何个体的流动性由两个不同空间尺度上的种群拥挤决定。通过这种方式，我们模拟了一些生物有机体（如贻贝）的行为，这些生物有机体倾向于在短距离内聚集作为防御策略，如果在大范围内存在高种群压力，则会强烈分散以优化觅食。我们进行随机模拟的粒子级模型的系统，并推导和分析一个连续的密度描述（一个非线性扩散方程）。在这两种情况下，我们表明，这种规模依赖行为的相互作用引起了丰富的空间格局的形成，从周期性的集群安排。在大多数情况下，这些星系团具有非常特殊的环状结构，即，我们详细讨论的是，在集群周边排列的生物。
英文摘要：
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological organisms (like mussels) that tend to cluster at short ranges as a defensive strategy, and strongly disperse if there is a high population pressure at large ranges for optimizing foraging. We perform stochastic simulations of a particle-level model of the system, and derive and analyze a continuous density description (a nonlinear diffusion equation). In both cases we show that this interplay of scale-dependent-behaviors gives rise to a rich formation of spatial patterns ranging from labyrinths to periodic cluster arrangements. In most cases these clusters have the very peculiar appearance of ring-like structures, i.e., organisms arranging in the perimeter of the clusters, that we discuss in detail.
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