1988 , Vol. 3 >Issue 3: 271 - 280

Zipf定则及其广延在自然资源数量计算中的应用

• 中国科学院、国家计划委员会地理研究所

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

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• Institute of Geography, Chinese Academy of Sciences

Online published: 1988-09-25

### Abstract

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 Pr -= P0/rto Pr = P0/rbin which, P0-the amount of the first order in a non-continuous series; Pr-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, 0<1, b>1, 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.
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