城市化水平增长曲线的类型、分段和研究方法

城市化水平增长曲线可以分为S形和J形2大类别，其变化特征、动力学背景及研究方法也不尽相同。城市化曲线研究可以分为唯象分析和唯理分析2大途径，唯理研究包括城一乡人口异速生长、城一乡人口替代以及城乡人口迁移和转换3种路径，目前这些方法主要用于S形曲线研究，对J形曲线的探索不够深入。S形曲线是一种奇对称曲线，其模型导数却是一...

On the Urbanization Curves:Types,Stages,and Research Methods

The curves on the change of level of urbanization over time are called urbanization curves,which are in fact models of the progress of urbanization based on empirical evidences from developed countries and developing countries.There are two types of urbanization curves.One is S-shaped curve,and the other,J-shaped curve.The S-curve can be modeled with the logistic function,while the J-curve cannot be described by the logistic function.The former is applicable to the developed countries,whereas the latter is applicable to the developing countries.So far,there have been more studies on the S-shaped curve.However,fewer studies have been devoted to the J-shaped curve of urbanization.Consequently,we know little about the general principle on the J-shaped curve and its underlying rationale,which remain to be further explored in the future.In this paper,various studies on urbanization curves are systemized to form a framework of models on the level of urbanization.The logistic curve was once divided into three stages by Northam(1979): initial stage,acceleration stage,and terminal stage.However,the Northam’s proposal is just a phenomenological theory with several defects: first,the definition of ’acceleration stage’ is not correct;second,there are no theoretical basis and critical scale for the divisions.It can be proved that the logistic process falls into four phases.Taking half of urbanization level capacity as a tipping point,the logistic curve is divided into two stages: acceleration stage(urban majority) and deceleration stage(urban minority).The tipping point can be determined by two methods of elementary mathematics.Then the two stages are respectively divided into two sub-stages by means of the exponential law of urban-rural ratio with a parameter as characteristic length.Now,urbanization process can be divided into four stages: initial stage,acceleration stage,deceleration stage,and terminal stage.Also it can be divided into three stages: initial stage,celerity stage(including acceleration stage and deceleration stage),and terminal stage.Two methods are always applied to the research of urbanization curves and the related urbanization dynamics.One is phenomenological analysis,and the other,theoreticalogical analysis,which consists of three approaches: urban-rural allometric growth,urban-rural population replacement,and urban-rural population interaction dynamics.Urban-rural allometric growth analysis is a kind of scaling analysis.Urban-rural population replacement suggests a new dynamical analysis.Urban-rural interaction comprises linear dynamics and nonlinear dynamics.The linear dynamics is based on the well-known Keyfitz-Rogers model,whereas the nonlinear dynamical analysis can be employed to interpret the similarities and differences between the S-shaped and J-shaped curves.China’s urbanization process can be described with the J-shaped curve rather than the S-shaped curve.The studies on the urbanization curves will be significant for understanding the dynamical mechanism and essence of Chinese urbanization.