増殖過程の微視的構造から得られた波動的成長曲線

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If we call a temporal changing process of a value x of a phenomenon X a growth curve, when the value x at time t is determined only by time t, in other words, when x is expressed by the equation: x=f(t) then many types of growth curves are found in many branches of studies, demography, biology, economics, geography, statistics, and so on. Basis assumptions for obtaining the growth curves could be classified into two groups. In the first group, the x is obtained from assumptions for behavior of the components of a phenomenon X, while in the second group, the X is obtained from that of the total amount of the components of a phenomenon X. Among these two assumptions, the former could be called microscopic structure of a phenomenon, and the latter macroscopic structure of a phenomenon. Hagerstrand's model for describing a spatial dispersion of information is regarded as a model obtained from the microscopic structure of spatial dispersion of information. In this paper, an expansion of the Hagerstrand's model is studied. In the Hagerstrand's model, a states of a person at a place in a region questioned (S) is determined by the position of the person who has an information initially (P_0), the effect of random choice of a person who accepts an information (E), that of floating grid (F), that of resistance (R), that of barrier (B) and the time (t). Therefore, the S will be able to be expressed by the equation: S=f(t/P_0, E, F, R, B) where S=1 when a person has accepted an information and S=0 when he has not accepted an information. The function f is, in this place, regarded as a function of t conditioned by P_0, E,F,R, and B. Here, if the duration of holding an information (D) and the number of despatching information at a time (N) are added to the function f shown above, a new function: S=f(t/P_0, E, F, R, B, D, N) will be obtained. The spatial distribution of persons who have accepted information at time t and the total number of the persons at time t, X(t) were obtained under the condition that R=1, D=1,2,3,4,5, ∞ and N=1,2,3,4,5, and without the condition B by simulations using a computer. Although the growth curve of X(t) is not described by a function of t, the general structure of X(t) is expressed by the following equation: X(t)=X(t-D)+X(t-D+1) + … +X(t-1)(1+N)-X(t-D)-O(t)-S(t) where O(t) is the number of informations which are not accepted by reason that the informations are sent to the persons who have already accepted the information, and S(t) is the number of the spill of the information despatched, from the region questioned. Table 4 and Figures 10 and 11 are the spatial distribution and the total number of person X(t) who have accepted an information. The growth curve of X(t) has fluctuations, while X(t) obtained from Hagerstrand's model has no fluctuation. The cause of appearance of the fluctuations is introduction of the condition D into the Hagerstrand's model. The expanded model would be utilized as the model of temporal change of spatial distribution of plants, epidemics, and so on.
流通経済大学の論文

著者

鈴木啓祐
流通経済大学

増殖過程の微視的構造から得られた波動的成長曲線

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