华中师范大学学报（自然科学版）2001，Vol.35Issue(2)：229-233,5.
城镇等级体系的Beckmann模型与三参数Zipf定律的数理关系 ——Beckmann城镇等级 - 规模模型的分形与分维
Mathematical relationships between the three-parameter Zipf law and the Beckmann model of city hierarchies
摘要
Abstract
A three-parameter Zipf's model,P(N)=C(N-α)-dz,is deduced out from the well-known Beckmann's model on city hierarchies, Pm=RKSm-1/(1-K)m,where C=P1［S/(S-1)］dz, α=1/(1-S), and dz=1-ln(1-K)/lnS. On the other hand,a formula on level of urbanization based on the Beckmann model, Z=KS/(K+S-1), implies that, S, the number of satellite towns around a city, ‘decreases’ along with the increase of urbanization level of a region, Z, for ( Z/ S)＜0. This paper makes a conclusion as follows: The ‘stairs’ of city-size hierarchies deriving from the central place theory will inevitably transform into the rank-size distribution with fractal nature because of urbanizational dynamics.关键词
城镇体系/城市规模分布/城市化/位序-规模法则/对称/幂律/分形分类
管理科学引用本文复制引用
陈彦光..城镇等级体系的Beckmann模型与三参数Zipf定律的数理关系 ——Beckmann城镇等级 - 规模模型的分形与分维[J].华中师范大学学报（自然科学版）,2001,35(2):229-233,5.基金项目
国家自然科学基金资助项目(40071035)及河南省自然科学基金资助项目(984071000). （40071035）
