Zipf定则及其广延在自然资源数量计算中的应用

吉弗定则（Zipf Theorem）具有相当广泛的解释功能,因此有可能用该定则去估算自然资源的数量分布形态。本文总结了吉弗定则的普适性,并对原式实施了广延,得出了一些很有启发的结论。首先将该定则从 P_r=P₀/r 扩大到 P_r=P₀/r^b,并从b的行为中去认识自然资源数量分布的特性,把原先b=1 的吉弗方式推广到b在非1情形下的各种方式。以我国的水资源为案例作了验证,取得了满意的结果。最后指出,进一步对于参数b进行数理解析,是深入认识各类资源形态分布机制的关键所在,并发现有可能找出吉弗定则与“奇异吸引子”之间的联系。

APPLICATION OF ZIPF THEOREM AND ITS EXTENSION IN QUANTITATIVE CALCULATION OF NATURAL RESOURCES

Zipf Theorem (Zipf, G. K., 1949) is a very valuable rule to express the morphological distribution of non-continuous series in human society or natural world. In our research, the Theorem seems to be the first use in the world for the quantitative calculation of natural resources. In this paper, we have applied the principle of Zipf Theorem to achieve more comprehensive explanation of non-continuous resources arrangement according to their order in the series. For instance, "rank-size" relation of species in spatial structure, distribution of city population, and so forth.Zipf Theorem has been extended to a new form including all of states. That isfrom P_r -= P₀/rto P_r = P₀/r^{bin which, P₀-the amount of the first order in a non-continuous series; P_r-the amount ofthe order r, r-number in the series; b-a key parameter discovered.If b = 1, it is equivalent to Zipf form. If b≠1 (e. g. b<1, b = 0, 01, b→∞), the curves of the series in graph would have various geometric shape. However, it is interesting that these curves have been the same family of Zipf Theorem. The research has already proved that the extension can exist on some universal basis. Also, we used annual average runoff of Chinese 26 rivers as the case study to examine the conclusion. The result is quite satisfactory. In our discussion, how to analyse the signification of value b and go further into the mechanism governing behaviour of the parameter b will be our new target. We have also discovered, a possible relationship between Zipf Theorem and "Strange Attractor" is existing.}