城市化水平Logistic方程参数性质的初步探讨

A Preliminary Approach to the Nature of the Parameter of Logistic Equation on Urbanization Level

本文从一般地理系统的动力学方程中引出城—乡人口异速生长模型及城市化水平的Ｌｏｇｉｓｔｉｃ方程，借助二者的联系揭示了城市化水平的模型参数与分形维数的关系。文章以实例说明Ｌｏｇｉｓｔｉｃ方程参数一般小于１，从而城市化水平的演进呈单增型定态图式。一个重要的结论是：地理系统出现混沌的前兆之一是分维暴胀。

The allometric growth model on urban-rural population and the Logistic equation on the level of urbanization were deduced from the same equations of general geographical system,by means of which the relationship between the Logistic parameter and the allometric coefficient was discovered ,and the latter is related to fractal dimension .It was illustrated that the Logistic parameter value was always less than 1,which means that there is no chaos in a process of urbaniztion.A important conclusion can be reached that the omen of chaos is that the fractal dimension of a geographical system rises suddenly and sharply.