2009 , Vol. 64 >Issue 2: 177 - 188

• 1. 同济大学建筑与城市规划学院, 上海200092;
2. 洛阳市规划建筑设计研究院, 洛阳471000

修回日期: 2008-11-10

网络出版日期: 2009-02-25

Delimiting the Stages of Urbanization Growth Process: A Method Based on Northam's Theory and Logistic Growth Model

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• 1. College of Architecture and Urban Planning, Tongji University, Shanghai 200092, China;
2. Luoyang Urban Planning and Architecture Design Institute, Luoyang 471000, Henan, China

Revised date: 2008-11-10

Online published: 2009-02-25

Supported by

National Key Technology R&D Program, No.2006BAJ11B08; National Natural Science Foundation of China, No.50778126

### 摘要

Northam 认为城镇化呈“s” 型曲线发展, 其过程可划分为三个阶段, 这为众多研究证实和引用, 但其阶段分界点长期缺乏严格的数学定义。运用高等数学方法, 推演出城镇化 “s” 型曲线的Logistic 增长模型关于时间变量t 的方程表达式, 并通过定性与定量分析, 推导 出该曲线的三个特征点及其数学表达式。对Northam 城镇化发展阶段划分思想进行进一步的讨论, 提出城镇化发展“s” 型曲线上两个曲率最大点为城镇化三个阶段的分界点; 验证了在拐点处城镇化发展速度最大加速度为零, 之前速度逐渐加大, 之后速度逐渐减小; 给出了阶 段划分点、拐点和第二阶段历时与平均速度的计算公式。选择日本和其他22 个国家城镇化历史数据进行拟合分析, 城镇化阶段划分结果与相关研究非常吻合, 并且符合世界城镇化发展 的总体趋势, 还特别证明并指出2004 年中国城镇化发展已经出现速度拐点, 验证了模型推导的结果。最后讨论了该方法的适用性和局限性。

### Abstract

Northam conceptualizes the urbanization course with an S-shaped curve, which was divided into three stages. Although this theory has been widely validated and referred to by various researchers, the dividing points between each stage are not explicitly defined in mathematical method. This essay is to deduce the equation of the Logistic model of urbanization level according to the variable t (time series) by mathematical methods. Through qualitative and quantitative studies, it proves that the Northam curve has three characteristic points which are the inflexion point and two biggest curvature points. It is validated that the urbanization growth rate attains the maximum while the acceleration is down to zero at the inflexion point, as the urbanization growth is accelerated before reaching the point and decelerated afterwards. Developed further from the Northam's theory of three phases of urbanization, the two biggest curvature points are identified to divide the urbanization growth course into three stages. This essay also presents the mathematical formula of the three characteristic points and the duration and the mean growth rate at the second stage. By modeling the urbanization processes of Japan and other 22 countries with historical data, it is proved that the result tallies with other relevant studies and the world urbanization development trends. It further indicates that the China's urbanization reached its inflexion point in 2004. Finally, it discusses the applicability and the limitation of this method.

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