The fact that up to the 1960s world population growth had been characterized by a hyperbolic trend was discovered quite some time ago. A number of mathematical models describing this trend have already been proposed. Some of these models are rather compact but do not account for the mechanisms of this trend; others account for this trend in a very convincing way, but are rather complex. In fact, the general shape of world population growth dynamics could be accounted for with strikingly simple models like the one which we would like to propose ourselves: dN/dt = a (bK N) N (1); dK/dt = cNK (2), where N is the world population, K is the level of technology/knowledge, bKcorresponds to the number of people (N), which the earth can support with the given level of technology (K). Empirical tests performed by us suggest that the proposed set of two differential equations account for 96.2 99.78% of all the variation in demographicmacrodynamics of the world in the last 12,000 years. We believe that the patterns observed in pre-modern world population growth are not coincidental at all. In fact, they reflect population dynamics of quite a real entity, the world system. Note that the presence of a more or less well integrated world system comprising most of the world population is a necessary precondition, without which the correlation between the world population numbers generated by hyperbolic growth models and the observed ones would not be especially high. In fact, our findings could be regarded as a striking illustration of the fact well known in complexity studies that chaotic dynamics at the microlevel can generate a highly deterministic macrolevel behavior. Against this background it is hardly surprising to find that the simplest regularities accounting for extremely high proportions of all the macrovariation can be found just for the largest possible social system the world system.
The dynamics of population by settlements in the Guba-Khachmaz economic-geographical region
