中文摘要：

为了研究城市化进程中城市和农村人口的变化情况,建立了一个Logistic微分方程模型,讨论了该模型解的有界性、平衡点的存在性和稳定性,并利用Dulac函数法给出了非平凡周期解的不存在性.

英文摘要：

To study the changes between the urban population and the rural population in the process of urbanization, a Logistic differential equation model was formulated. The boundedness of solution, the existence and stability of equilibria were investigated and the nonexistence of nontrivial positive periodic solution was studied using Dulac function method.