群体迁移行为的理论与实证研究

Theoretical and empirical studies on group behaviors

人类行为往往取决于经济社会的某种趋势性影响,对其动力学的定量描述和准确理解是当前复杂系统研究的热点.本文提出由迁移距离,迁移人口年龄和迁出地经济人口密度所描述的群体迁移欲望函数,及广义势.借助于朗之万方程,将其转变为Hamilton-Jacobi方程,从而对群体决策行为进行统计理论分析.采用高维最陡降线的方式求解Hamilton-Jacobi方程.其解的形式揭示了群体迁移过程中信息熵随着迁移群体年龄的变化呈现一个单峰;信息熵对迁移距离的二阶导随迁移距离而穿零变化(对应一种相变);信息熵随着经济人口密度也呈现单峰.进一步分析信息熵的这些变化规律所蕴含的意义及其机理,从而获得对人类群体迁移行为的新理解,为政府管理提供参考和启示.

Human behaviors are usually determined by some social and/or economic trend. In the past few years, many attempts have been made, in the field of complex scientific systems, to describe the dynamics of these behaviors quantitatively and have an accurate understanding of the corresponding mechanisms. In this paper, a generalized potential,that is, a migration desire function defined by the age of the migrating people, the migrating distance, and the so-called economic-population density of the emigration area, is proposed. It can be transformed into Hamilton-Jacobi equation by using a random dynamical method, Langevin equation, so that the decision-making behavior can be investigated,based on a statistic framework during a group migration process. By taking use of the multi-dimensional steepest descent method, the Hamilton-Jacobi equation is solved; the solution shows that the information entropy of the system varies,leading by a single peak, as the age of the migrating people increases. It also demonstrates that the second derivative of the migrating distance to the information entropy has a change of zero-crossing（which actually means a phase change）.The third characteristic of the solution is that the information entropy follows another single peak as the economicpopulation density increases. A deeper analysis reveals the significance behind these findings and the corresponding mechanisms. So some new understandings of the group human behaviors can be obtained, and some worthy references can be provided for some related administrative offices.