THE LOCATION PROCESS OF POPULATION DYNAMICS AND FRACTAL FORM OF CITIES: A THEORETICAL APPROACH TO A MATHEMATICAL MODEL FOR URBAN GROWTH
LIU Ji-sheng1, CHEN Yan-guang2
1. Department of Geography, Northeast Normal University, Changchun 130024, China;
2. Department of Urban and Environmental Sciences, Peking University, Beijing 100871, China
Abstract This paper starts with the Naroll-Bertalanffy's hypothesis of the allometric growth of urban-rural population, namely and Sherratt's model about the distribution of urban population density, which are both based on the Christaller-lösch's central place hypothesis and the hypothesis of supposing the regional population movement on the ideal land surface is similar to Brownian movement process. We derive the well-known mathematical model equation about the special dynamic of population distribution and the time-space process of urban diffusion. The author indicate the relationship between DBM model and DLA model. Basen on the above analysis, this paper then gives the concrete method of DLA-DBM simulation about urban growth and form, compares the simulant function for urban form between DLA model and DBM model, and considers DBM model is much better than DLA model. At the last part, the author expounds the relationships between urban growth, man-land relationship and fractal form. We think that the urban-growth DLA-DBM simulation makes the fractal form of urban land utilization by using the population location-choice principle and urban dynamic principle in fact. Then the author discusses the two parts of urban-growth dynamic principle-Fourier diffusion movement and Logistic growing progress of urban growth and presents the Laplace equation. At the end of this part, three fundamental principles are suggested as follows:①Information entropy maximization principle, which can be used to explain Clark's model and Sherratt's model on urban population densities;②Allometric growth principle, including urban-rural population relationships and urban area-population relationships; ③Logistic growth principle, which keeps inner link with both Clark's model and Sherratt's model. In the end, this paper points out the problem awaiting solution-the converting mechanism of Clark-Smeed model.
2002, Vol. 17 
