P(論文)

The purpose of this study is to analyse the change of the distribution of population in an urban area. An urban area was devided into many small areas, and the change of the population density of the small areas are examined by some simulations based on two models, exact and stochastic models. The models used in these simulations were built under a supposition that the population density in the ith area (R_i) at time t, D_<it> was determined by the population densities in the ith area and the areas surrounding the area (R_i(q), (q=1, 2, …, m_i)) at time t-1,D_<i t-1> and D_i (q)_<t-1>, where q was the number of an area surrounding the ith. area. Therefore, in the model proposed here, the population density in the ith area at time t was determined by the following equations : D_<it> = D_<it-1> + ΔD_<i(t)> (when D_<i(t)> < 0, D_<i(t)>=D^* (≧0)) ΔD_<i(t)>=φ(D^^～_<i t-1>) φ(D^^～_<i t-1>=φ{D_i(0)_<t_1>, D_i(1)_<t-1>, …, G_i(q)_<t-1>, ……, D_i(m_i)_<t-1>} or D_<it>=D_<i t-1>+D_<i(t)> (when D_<i(t)> 0, D_<i(t)>=D^* (0)) ΔD_<i(t)>=φ(D^^～_<i t-1)+e φ(D^^～_<i t-1>)=φ{D_t(0)_<i-1>, D_i(1)_<t-1>, …, D_i-(q)7>_<t-1>, ……, D_i(m_i)_<t-1>} where ΔD_<i(t)> was the diffenence between D_<i t-1> and D_<it> (or D_<it>-D_<i t-1>), D_i(0)_<t-1> was D_<i t-1>, m_i was the largest number of the area among the numbers of the areas surrounding the ith area, and e was the residual whose value was given at random. The former model is the exact model of the simulation model, and the latter one is the stochastic model. If the form of the founction φ(D^^～_<i t-1>), D^* and e are specified, the D_<it> is determined by these models. In this paper, φ(D^^～_<i t_1>) was defined by φ(D^^～_<i t-1>)=1/2[<max>___q {D_i(O)_<t_1>, D_i(1)_<t-1>, …, D_i (q)_<t-1>, …, D_i(m_i)_<t-1>} + <min>___q {D_i(0)_<t-1>, D_i(1)_<t-1>, …, D_i(q)_<t-1>, …, D_i(m_i)_<t-i>}] Here, this type of model was called "contageous model" because the effect of the states of a phenomenon in the areas other than the ith area were given to the state of a phenomenon in the ith area. Incidentally, Hagerstrand has built his models for explanation of diffusion of information. In his model, the attitude of a person to a specific part of his action in an area is affected by the information given to him by other persons in other areas. Therefore, this model can be also regarded as a contageous model. According to the results of the simulations of the change of distribution of population in an urban area by the model proposed here, it was found that the model explained successfully the change of the distribution of population in an urban area, and especially it depicted very clearly the mechanism by which the population density in the center in an urban area becomes relatively lower, as the size of urban area becomes large.