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Trends and forecasting models of population growth on the base of multifractal dynamics


А.N. Kudinov – Dr.Sc. (Phys.-Math.), Professor, Tver State University. E-mail: V.N. Ryzikov – Ph.D. (Phys.-Math.), Associated Professor, Tver State University. E-mail: V.P. Tsvetkov– Dr.Sc. (Phys.-Math.), Professor, Tver State University. E-mail: I.V. Tsvetkov– Dr.Sc. (Eng.), Professor, Tver State University. E-mail:

In the work, the population growth trends were defined, and growth behavior up to 2103 was forecasted based on the multifractal dynamics model (MDM). The basic equations of multifractal model of population growth were obtained. All possible population growth processes were classified based on the multifractal dynamics model. The multifractal dynamics model parameters were calculated based on experimental data on population size obtained over the last 62 years. Three periods where the population growth behavior was close to the linear law were found out. It was demonstrated that the rate of growth increased over the three periods from 0.0488 billions of persons per year, in the first period to 0.0808 billions of persons per year, in the third period. Increase in duration of periods was observed. The graph of function h given in Fig. 6 is indicative of a self-similar growth character. Annually, the waves of population growth occur forming a well defined piecewise-linear trend over the 20-30 periods. The population growth curve fractal dimension values calculated by us are much different from D0 wherein the growth stops. This fact explicitly states the continuation of a population growth trend in the near term. In this work, the growth in population for the next 90 years was forecasted based on the MDM. This forecast implies that by 2024, the universe will be 9.606 billions of persons, by 2072 – 12.242 billions of persons, and by 2102 – 14.973 billions of persons. Doubling of population size of 2011 (7 billions of persons) should take place in 2092±1. The probability of population stabilization by this time is an open ended question.


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