of the Russian Academy of Sciences, Ekaterinburg

This publication is devoted to the theory of demographic cycles ad-vanced in researches of many authors. F. Braudel named these cycles as ‘general cycles’, and R. Cameron used concept ‘logistics cycles’. The author has constructed the mathematical model of a demo-graphic cycle. The size of sowing areas, population, the number of peasants and handicraftsmen are basic variables of this model. The level of life, reserves of grain, a sale of grounds, a growth of large property, a transition of peasants to tenantry or handicraftsmen and other factors of the socio-economic relations are taken into account. Generally, the model represents an analogue of system of three inte-gro-differential equations. The verification of the model is made on the material of the history of Ancient China. The good concurrence of the design data to the data of the account of the population is established. Population growth with limited amount of resources and with a fixed production technology can be described by a ‘logistics equation’