收稿日期: 2008-04-08
修回日期: 2008-11-10
网络出版日期: 2009-02-25
基金资助
国家科技支撑计划课题(2006BAJ11B08); 国家自然基金项目(50778126)
Delimiting the Stages of Urbanization Growth Process: A Method Based on Northam's Theory and Logistic Growth Model
Received date: 2008-04-08
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
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。
关键词： 城镇化; 发展阶段; Northam 理论; Logistic 增长模型; 阶段划分方法
王建军, 吴志强 . 城镇化发展阶段划分[J]. 地理学报, 2009 , 64(2) : 177 -188 . DOI: 10.11821/xb200902005
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.
[1] Northam, RM. Urban Geography. 2nd edn. New York: John Wiley & Sons, 1979. 65-67.
[2] Chen Yanguang, Zhou Yixing. Logistic process of urbanization falls into four successive phases: Revising Northam's Curve with new spatial interpretation. Economic Geography, 2005, 25(6): 818-822.
[陈彦光, 周一星. 城市化Logistic 过程的阶段划分及其空间解释: 对Northam 曲线的修正与发展. 经济地理, 2005, 25(6): 818-822.]
[3] Mulligan G F. Logistic population growth in the world's largest cities. Geographical Analysis, 2006, 38: 344-370.
[4] Jiao Xiuqi. The "S" curve of world urbanization. City Planning Review, 1987, (2): 34-38.
[焦秀琦. 世界城市化发展的 S 型曲线. 城市规划, 1987, (2): 34-38.]
[5] Karmeshu. Demographic models of urbanization. Environment and Planning B: Planning and Design, 1988, 15(1): 47-54.
[6] United Nations. World Urbanization Prospects: The 2005 Revision. United Nations, New York, 2004.
[7] Li Xinyun, Zhang Xiaoqing, Wu Yulin. The parameter estimation method of urbanization people model and its application. Economic Geography, 1995, 15(4): 82-88.
[李新运, 张晓青, 吴玉林. 城市化人口模型的参数估计及应用实例. 经济地理, 1995, 15(2): 82-88.]
[8] Wang Yuanfei, Zhang Chao. Urbanization prediction in China with development parameter estimation method of logistic model. Economic Geography, 1997, 17(4): 8-13.
[王远飞, 张超. Logistic 增长模型参数估计与我国城市化水平预测.经济地理, 1997, 17(4): 8-13.]
[9] Bai Xianchun, Tang Deshan. The modification of logistic model and its application. Journal of Nanjing Institute of Technology (Natural Science Edition), 2004, 2(2): 15-20.
[白先春, 唐德善. Logistic 增长模型的修正及其应用. 南京工程学院学报(自然科学版), 2004, 2(2): 15-20.]
[10] Chen Yanguang, Guo Hongjian. A preliminary approach to the nature of the parameter of logistic equation on urbanization level. Journal of Xinyang Teachers College (Natural Science Edition), 1999, 12(1): 65-69.
[陈彦光, 郭红建. 城市化水平Logistic 方程参数性质的初步探讨. 信阳师范学院学报(自然科学版), 1999, 12(1): 65-69.]
[11] Chen Yanguang, Liu Jisheng, Fang Yangang. Utility-maximization, logit transformation and the basic mathematical models for analytical urban geography. Scientia Geographica Sinica, 2002, 22(5): 581-586.
[陈彦光, 刘继生, 房艳刚.效用最大化、Logit 变换和城市地理学的数量分析模型. 地理科学, 2002, 22(5): 581-586.]
[12] Chen Yanguang, Luo Jing. Derivation of relations between urbanization level and velocity from logistic growth model. Geographical Research, 2002, 25(6): 1063-1072.
[陈彦光, 罗静. 城市化水平与城市化速度的关系探讨: 中国城市化速度和城市化水平饱和值的初步推断. 地理研究, 2006, 25(6): 1063-1072.]
[13] Chen Yanguang, Zhou Yixing. Modeling the urbanization process of China by using nonlinear dynamic equations. Acta Scientiarum Naturalium Universitatis Pekinensis, 2007, 43(4): 542-548.
[陈彦光, 周一星. 城市化过程的非线性动力学模型探讨. 北京大学学报(自然科学版), 2007, 43(4): 542-548.]
[14] Chen Yanguang. Modeling the urbanization process of China using the methods based on auto-correlation and spectral analysis. Geographical Research, 2007, 26(6): 1021-1031.
[陈彦光. 中国城市化水平的自回归与功率谱分析. 地理研究, 2007, 26(6): 1021-1031.]
[15] Ledent J. Rural-urban migration, urbanization, and economic development. Economic Development and CulturalChange, 1982, 30(3): 507-538.
[16] Cook C J. Rural-urban migration rates and development: A quantitative note. Review of Urban & Regional Development Studies, 1999, 11(1): 63-75
[17] Berry B J L, Hall L S, Rodolfo Hernandez-Guerrero et al. Mexico's demographic transition: Public policy and spatial process. Population and Environment, 2000, 21(4): 363-383.
[18] Kozulj R. People, cities, growth and technological change from the golden age to globalization. Technological Forecasting & Social Change, 2003, 70: 199-230.
[19] Keyfitz, N. Applied Mathematical Demography. 2nd edn. New York: Springer-Verlag, 1985.
[应用数理人口学. 郑真真等译. 北京: 华夏出版社, 2000. 18.]
[20] Zhan Jifeng. The rural surplus labors transfer and its characters in Japan before World War II. Japanese Studies, 2002,3: 81-98.
[张季风. 战前日本农村剩余劳动力的转移及特点. 日本学刊, 2002, 3: 81-98.]
[21] Zhan Jifeng. The rural surplus labors transfer and its characters in Japan after World War II. Japanese Studies, 2003, 2:78-93.
[张季风. 战后日本农村剩余劳动力的转移及特点. 日本学刊, 2003, 2: 78-93.]
[22] Hao Shouyi, Wang Jiating, Zhang Huanzhao. Historic review of industrialization, urbanization and succession ofagro-land system in Japan. Japanese Studies, 2007, 1: 80-92.
[郝寿义, 王家庭, 张换兆. 日本工业化、城市化与农地制度演进的历史考察. 日本学刊, 2007, 1: 80-92.]
[23] Fu Hengjie. The urbanization model of Japan and its revelation to China. Japan Problem Studies, 2003, 4: 18-21.
[付恒杰. 日本城市化模式及其对中国的启示. 日本问题研究, 2003, 4: 18-21.]
[24] Wang Dongmei. The comparison between the urbanizations in Japan and USA and its revelation to China. ChineseRural Economy, 2003, 9: 69-76.
[汪东梅. 日本、美国城市化比较及其对我国的启示. 中国农村经济, 2003, 9:69-76.]
[25] Online Historical Population Reports (OHPR). Census 1801-1931.
[M/OL].
[2004-05-28]. http: //www.histpop. org/ohpr/servlet/.
[26] Xiao Huiying. Urbanization, floating population and economic growth. World History, 1997, (5): 62-71.
[肖辉英. 德国的城市化、人口流动与经济发展. 世界历史, 1997, (5): 62-71.]
[27] Wang Jiabao. The French Population and Society. Beijing: Chinese Youth Press, 2005.
[王家宝. 法国人口与社会. 北京: 中国青年出版社, 2005.]
[28] Wang Jianjun, Wu Zhiqiang. Urbanization in main countries in the world after 1950: Character styles and classes.Urban Planning Forum, 2007, 172(6): 47-53.
[王建军, 吴志强. 1950 年后世界主要国家城镇化发展: 轨迹分析与类型分组. 城市规划学刊, 2007, 172(6): 47-53.]
[29] Wang Xu. The patterns of american urban development: From urbanization to metropolitanization. Beijing: TsinghuaUniversity Press, 2006. 33-40, 200-214.
[王旭. 美国城市发展史: 从城市化到达都市区化. 北京: 清华大学出版社,2006. 33-40, 200-214.]
[30] Atack Jeremy, Passell Peter. A New Economic View of American History. 2nd edn. New York: Norton W W, 1996.
[新美国经济史. 罗涛等译. 北京: 中国社会科学出版社, 2000. 145-210.]
[31] National Bureau of Statistics of China. China Statistical Yearbook 2007. Beijing: China Statistics Press, 2007.
[2008-05-07]. http: //www.stats.gov.cn/tjsj/ndsj/2007/indexch.htm.]
[中国国家统计局. 中国统计年鉴2007.北京: 中国 统计出版社, 2007.
[2008-05-07]. http: //www.stats.gov.cn/tjsj/ndsj/2007/indexch.htm.]
[32] Treivish A, Brade I, Nefedova T. Russia cities at a crossroads. GeoJournal, 1999, 49: 115-127.
[33] Nefedova T, Treivish A. Differential urbanization in Russia. Tijdschrift voor Economische en Social Geography, 2003,94: 75-88.
[34] Li Qiuyuan, Meng Deshun. Property of logistic curve and its application in the analysis of plant growth. Journal of Northwest Forest University, 1993, 8(3): 81-86.
[李秋元, 孟德顺. Logistic 曲线的性质及其在植物生长分析中的应 用. 西北林学院学报, 1993, 8(3): 81-86.]
[35] Cui Dangqun. Analysis and making good fitting degree test for logistic curve regression equation. Application of Statistics and Management, 2005, 24(1): 112-115.
[崔党群. Logistic 曲线方程的解析与拟合优度测验. 数理统计与管理, 2005, 24(1): 112-115.]
[36] Xu Fuxia, Li Xiumin, Xu Hongmei et al. A study of epidemic Logistic model. Chinese Journal of Health Statistics,2007, 24(2): 168-170.
[徐付霞等. 传染病的Logistic 模型研究. 中国卫生统计, 2007, 24(2): 168-170.]
/
| 〈 |
|
〉 |