基于种群生态学模型的产业集群演进规律研究——以时滞为参数的动态分析

Study on the Evolutionary Trajectory in Industrial Clusters Based on the Population Ecological Models——Dynamical Analysis with Delay as a Parameter

笔者基于生态学视角,对一类描述产业集群的动态发展过程的数学模型进行了改进,在集群企业间的影响系数和环境对企业自身的密度限制项中加入了时滞,对应集群企业之间的竞争关系、互利关系和上、下游关系得到了新的泛函微分方程模型。并以时滞为参数,研究了系统正平衡点的稳定性和系统的Hopf分支的存在性条件,探讨了产业集群的演进规律及相应的对策建议。

From the ecology perfective,a series of mathematical models describing the dynamic process of development in industrial clusters were composed.Delays were added in the reflection coefficient and environmental density restrictions of corporations in industrial cluster.According to the competitive relationship as well as mutually beneficial relation and upstream downstream relation of the corporations in industrial cluster,a series of new functional differential equations were derived.Discussing the stability of positive equilibrium and the conditions for the existence of Hopf bifurcation of the system,we studied the evolutionary trajectories of industrial clusters and some suggestions were pointed out.