区域PREE系统演化的非线性特征研究

Study on Nonlinear Characteristics in Evolution of Regional Population-Resources-Environment-Economy System

为了整体把握区域发展的演化特征,建立了区域PREE系统整体演化模型;通过分析各子系统在临界点附近的协同作用机制,得出序参量子系统的演化方程;针对序参量子系统中的扰动因素,在方程中加入扰动项进行随机性分析,解得序参量子系统演化概率分布的定态解;最后,在定态解的基础上,得出序参量子系统广义势函数的表达式及其实际意义.研究结果表明,复杂的区域PREE系统的整体演化轨迹可通过分析其序参量子系统的演化来把握,同时可以从序参量子系统演化概率分布的定态解中得出序参量子系统的广义势函数,这将为定量分析区域PREE系统的稳定性提供依据.

In order to know the whole information on evolution of region,considering the nonlinear action in regional PREE system,evolution model of regional PREE system is set up. Through analyzing the synergetic action in the subsystems near critical point, evolution equation of order parameter subsystem is abtained. Adding disturbing to the equation and analyzing stochastic process, stationary state solution of probability distribution for order parameter subsystem is abtained too. Finally, the mathematic expression and practical sense of generalized potential fouction for order parameter subsystem is gotten. The result shows that evolution orbit of complicated regional PREE system can be known through analyzing evolution of order parameter subsystem and generalized potential fouction for order parameter subsystem can be gotten through analyzing stationary state solution of probability distribution. Then it can provide quantitative basis for analyzing stability of regional PREE system.