基于非线性动力系统的产业结构分析

The Analysis of Industrial Structure Based on Non-linear Dynamical Systems

当一个动态对比结构满足广义Lotka-Volterra模型时,可以自然地建立关于该结构的对比度指标的二阶常微分方程。非线性的广义Lotka-Volterra模型蕴含一个线性动力系统,通过该线性动力系统,极小二乘法同样能够解决广义Lotka-Volterra理模型的参数估计问题。数值试验表明湖南省第三产业与其他两个产业建立的对比结构满足广义Lotka-Volterra模型,实证模型说明湖南省第三产业的发展动力来源于其自身,但受到其他两个产业的抑制。

When a dynamical contrast structure satisfies a generalized Lotka-Volterr model, a 2-order ordinary differential equation of contrast is naturally established. The least square method is able to estimate the parameters in a generalized Lotka-Volterr model by using a linear dynamical system which comes from that generalized Lotka-Volterr model. Data show that the contrast structure of the service sector and other two sectors in Hunan province fit a generalized Lotka-Volterr model. A practical model reveals that the service sector in Hunan province is promoted by itself while it is suppressed by other two sectors.