地理科学 ›› 2000, Vol. ›› Issue (6): 528-533.doi: 10.13249/j.cnki.sgs.2000.06.528

• 论文 • 上一篇    下一篇

分形城市引力模型的一般形式和应用方法 ——关于城市体系空间作用的引力理论探讨

刘继生1, 陈彦光2   

  1. 1. 东北师范大学地理系, 吉林 长春 130024;
    2. 北京大学城市与环境学系, 北京 100871
  • 收稿日期:1999-12-21 修回日期:2000-06-14 出版日期:2000-11-20 发布日期:2000-11-20
  • 基金资助:
    国家自然科学基金(49771035)资助项目。

The Gravitational Models of Franctal Cities: Theoretical Basis and Applied Methods

LIU Ji-sheng1, CHEN Yan-guang2   

  1. 1. Departemnt of Geography, Northeast Normal University, Changchun, Jilin 130024;
    2. Department of Urban and Environmental Science, Peking University, Beijing 100871
  • Received:1999-12-21 Revised:2000-06-14 Online:2000-11-20 Published:2000-11-20

摘要: 基于分形思想和城市规模—产出关系推导出城市引力模型的一般形式Iij=GijMαiiMαjjR-bij,论证了参数αb的分维性质,并将引力系数定义为Gij=G|Rij|/(1+Sij),式中Riji、j两城市的相关系数,Sij为二者的相似系数,G为量纲转换系数。以长春城镇体系和郑、汴、洛点—轴系统为实例说明了模型的应用方法,并指出了城市引力数值的相对性特征。作者发现,城镇体系各要素的引力之和 ,在一定时空条件下满足位序—规模法则F(k)=F1K-q(k=1,2,…,n);这也表明,借助引力计算可以揭示城市体系某些隐含的地理规律。

Abstract: The theoretical foundation is laid and the applied methods are demonstrated for the gravitational models of fractal cities. The generalised urban gravitation expression is derived out as Iij=GijMαiiMαjjr-bij by means of the geographical fractal theory, especially, the city size-output relationship, y=CPα. The parameters, α and b, are made clear to have some meanings of fractal dimension, and the gravitational ceofficient is defined as Gij=GCiCj|Rij|/(1+Sij),where G is a dimensional transformation coefficient, C is a proportional coefficient, Rij is a coefficient of correlation, and Sij is a coefficient of similarity. The gravitational theory developed by the authors in the paper is applied to the urban system of Changchun in Jilin and the cities of Zhengzhou, Kaifeng,and Luoyang in Henan, China, to show how to use the gravitation models in practice, and based on the examples mentioned above, it is discovered that the resultant of gravitational forces between a city and each of the other cities in an urbon system conforms to the rank-size rule in due conditions, i.e., Fi(k)=F1k-q,where is rank, and F1 and q are parameters.

中图分类号: 

  • K928.5