城市人口密度衰减的分形模型及其异化形式——对Clark模型和Sherratt模型的综合与发展

The Fractal Model of Urban Population Density ——Decay and Its Related Forms:Derivation and Synthesis

  • 摘要: 从城市系统的一般方程出发,导出城市人口密度衰减的分形模型(ρ(r)∝rD-d),进而提出城市人口空间分布的Weibul型公式(P(r)/P0=1-exp[-(r/r0)D]),基此将传统的城市人口密度衰减模型由指数型(e-r/r0)和Gauss型(e-(r/r0)2)推广到一般形式(e-r/r0)δ,并揭示了它与分形模型的内在关系。

     

    Abstract: The fractal model of urban population density decay,ρ(r)∝r D-d ,was deduced from equations of a general urban dynamic system.On condition that the fractal nature of urban population has degenerated,a Weibull-model-like model of spatial distribution of urban population could be set up as P(r)p 0=1-exprr 0) D,from which a new general model of urban population density,ρ(r)=ρ 0 exp rr 0) D,was derived: when D=1,the new model becomes Clark model,ρ(r)=ρ 0 exp (-rr 0);and when D=2,it b...

     

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