基于互相关函数的分形城市引力模型——对Reilly-Converse引力模型的修正与发展

A Fractal City-Gravity Model Based on Correlation Function Revision and Development of Reilly-Conver

摘要: 引入时间函数Ｑ＝ｆ（ｔ）和时滞参数τ，借助互相关函数Ｒ（τ）＝∫ｆｉ（ｔ）ｆｊ（ｔ＋τ）ｄｔ，将城市引力模型Ｉｉｊ＝ＧＱｉＱｊｒ－ｂ由瞬间关系推广到相关过程，化为具有分形特征的引力模型Ｆｉｊ（ｒ，τ）＝ＧＲｉｊ（τ）ｒ－Ｄｉｊ，其中Ｇ被定义为城市间的最大相关系数，Ｄ（由ｂ推广而来）具有广义的分形维数性质。

Abstract: A new type of gravity model of cities, F(r,τ)=GR ij (τ)r -D ,was deduced from Reilly-Converse's model, I ij =GQ iQ jr -b ,through introducing time function,Q=f(t),and time-delay parameter,τ,to the latter,and in the former, R ij (τ)=∫f i(t)f j(t+τ) dt is a correlation funtion.The gravity coefficient,G,was defined as the maximum correlation coefficient of the variables Q i and Q j ,and the exponent,b,proved to be a generallized fractal dimension.