论文标题
移民作为复杂系统的无限种群：自我调节
Infinite populations of migrants as complex systems: self-regulation
论文作者
论文摘要
提出并研究了一个模型，描述了到达$ x \ subseteq \ mathbf {r}^d $，$ d \ geq 1 $的无限人口。这两种行为都以状态依赖性率随机发生。也就是说，根据他们的几何形状，现有的移民击退并吸引了新移民，这使得人口成为复杂的系统。它的状态是适当的配置空间上的概率度量，并且通过求解相应的fokker-planck方程来获得其演变$μ_0\至μ_t$。主要结果是结论是，这种状态的演变保留了其亚允许性，因此由于粒子间排斥而发生了局部自我调节（抑制聚类） - 无论范围很小。还讨论了借助此结果研究拟议模型的进一步可能性。
A model is proposed and studied describing an infinite population of point migrants arriving in and departing from $X\subseteq \mathbf{R}^d$, $d\geq 1$. Both these acts occur at random with state-dependent rates. That is, depending on their geometry the existing migrants repel and attract the newcomers, which makes the population a complex system. Its states are probability measures on an appropriate configuration space, and their evolution $μ_0 \to μ_t$ is obtained by solving the corresponding Fokker-Planck equation. The main result is the conclusion that this evolution of states preserves their sub-Poissonicity, and hence a local self-regulation (suppression of clustering) takes place due to the inter-particle repulsion -- no matter of how small range. Further possibilities to study the proposed model with the help of this result are also discussed.
