关键词: 城市体系, 异速生长, C-D函数, 分维, 郑州市, 城市结构

Abstract: A Cobb-Douglas-function-type model on cities as systems is derived from general expressions on urban dynamic systems, y=kf_i(x₁, x₂,..., x_n), the model can be named C-D function of cities and written as y=μ∏x_ii^σ_i,where x_i(i=1, 2,..., n) represents some kind of measure on cities, y is output in some sense, k and μ both proportionality coefficients. Throught the allometric relationship between two elements of cities, x_i～x_j^α_ij, the C-D function can be transformed into the two-variable expression, y=η(x_i^b_i) (x_j^b_j). A number of equations of fractal dimension are deduced out such as α_ij=D_i/D_j=σ_j/σ_i=b_j/b_i, σ_iD_i=σ_jD_j. It is proved that the equation. σ_i/(w_ix_i)=σ_j/(w_jx_j), should be met in order to optimize urban structure and function. Taking the city of Zhengzhou as example, the models presented and advanced are verified and vindicated.

Key words: urban system, allometric growth, C-D function, fractals, Zhengzhou city, urban structure