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Modeling of the relationship between the Earth population growth and the electric energy production processes

The actual problem of an adequate mathematical description of the world development global processes trends is studied on the example of the Earth population growth and the production (consumption) of the electric energy. Various models used to describe the past, present and future of the various processes in nature, technology and economics are considered. It is shown that these processes are well described by the equations obtained during solving differential models with exponentially growth rates decaying in time. These models take into account the currently accepted doctrine of sustainable development of the world system using energy saving technologies, preserving environmental safety and using renewable energy sources. The similarity of the studied global processes and the possibility of their description by one criterion equation are established. At the same time their dynamics is characterized by different speeds. The first period is characterized by a rapid growth. After the inflection point the growth rates slow down but the volumes increase significantly and a gradual saturation occurs. The influence of the model parameters on the character of the studied processes on the phase plane is estimated which significantly simplifies their analysis. It is shown that the process of the world population growth passed the inflection point in 1990 and is 29 years ahead of the world electricity production growth. But the growth rates of electricity production and its consumption per capita are significantly higher. Thus, new mathematical models are proposed to describe the dynamic series of the Earth population growth, world production and electric energy consumption per capita. The obtained mathematical models have been in good agreement with statistical data for 60 years since 1960 and have high values of the determination coefficient. The studied processes prediction for the long-term period up to 2050 was made with their help. The results of the prediction do not contradict the results of other authoritative studies using the global processes inertial development model. Read more...