@MISC{Nefedov_theelementary, author = {Sergey Nefedov and Ural Department}, title = {The Elementary Model of Population Growth}, year = {} }

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Abstract

Many works are devoted to study of population dynamics in an agricultural society with the help of mathematical models (For example: Komlos and Artzrouni 1990, Steinmann, Prskawetz and Feichtinger 1998, Kögel and Prskawetz 2001). However many models contain unknown coefficients, which influence their behavior. In this brief note we offer the elementary differential model, which has not uncertain parameters. Let N(t) is a population at the moment t. K(t) is stores of grain after the collecting of crop measured by an amount of minimum annual portions (1 portion is approximately 240 kg of a grain). r is a growth rate of the population in congenial conditions. A square of sowings and a crop depend on a population. They aspire to some constant, when the population grows. We shall consider, that the crop is determined by the formula P=aN/(N+d), where a and d are some constants. We use the usual logistics equation for exposition of population dynamics (1) dN dt