抵御集体风险视角下的人口聚集行为

On Population Aggregation Behaviors in the Perspective of Group Risk Resistance

本文构建了一个集体风险模型分析人口的聚集行为.在模型里,人口分布在具有一定网络结构的格点上,每个格点以一定的概率发生集体风险,设定抵御集体风险的阈值与该格点上的人口数存在幂律关系.每一时步,所有人口都提供一份资金用于防御集体风险的发生.假如某格点上的风险抵御总投资值小于该格点的阈值,则集体风险以随机的概率发生.格点上的每个人根据实际情况可以选择增加(减少)投资或者迁移到邻近格点.数值模拟结果表明,系统经过长时间演化后,人口分布将满足帕累托分布;人口数多的格点的人口分布则符合齐普夫定律.此外,人口分布规律的特征指数取决于风险发生概率、网络拓扑结构等系统参数.

A collective risk model is proposed in this paper to analyze the aggregation behavior of population. In the model, the population distributes in a lattice of a certain network structure, thus the collective risk usually outbreaks at each node with a certain probability. the threshold against the collective risk for each node has a power-law relation dependent on its population size at such a lattice point. At each time step, all the population provides a sum of funds to defense the collective risk. Once the total investment value is less than the threshold value at this lattice point, the collective risk takes place with a certain probability at random. Each person at the point can select to put either increased （or decreased） investment or migrate to the neighboring node according to the actual situation. The numerical simulation results show that the population distribution will satisfy the Pareto distribution after a long time evolution. And the population distribution with more population number lattice point accords with Zipf＇s law. In addition, the characteristic exponent of the population distribution regularities depends on the probability of risk occurrence and the system parameters like network topology.