为更真实地描述企业集群的动态演化规律,基于生态学角度考虑企业集群现象,建立了一类新的数学模型: 具有不同发展阶段和共生模式的企业集群系统,利用微分方程比较原理和构造适当的Lyapunov函数,得到了保证该系统持久性、概周期解存在唯一性和一致渐近稳定性的充分条件,获得一些新的结果,举例验证结果的合理性,并对结果分析作出相应的经济解释.

A new mathematics model to illustrate enterprise cluster with different development stage and symbiosis relationship is established based on ecological theory to describe the law of their dynamic evolution. By applying comparison theorem of differential equation and constructing a suitable Lyapunov function, the sufficient conditions for the permanence and uniformly asymptotically stability of a positive almost periodic solution of the system are obtained. Some new results are obtained. Moreover, we present numerical examples to illustrate the feasibility and effectiveness of our results and facilitate the interpretation of our mathematical results by economic views.