MATHEMATICAL MODELS OF MANIFESTATION OF SUSTAINABLE DEVELOPMENT OF TERRITORIES
A.K. Cherkashin
V.B. Sochava Institute of Geography, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia
Keywords: geographical environment, national wealth, composition and structure of assets, rental income, capitalization of savings, dynamics of integrated geosystems
Abstract
Sustainable development is considered as a process of preserving and safely overcoming the opportunities of the geographical environment, understood as a set of conditions and resources both natural and industrial and social origin. The state and sustainable change of the geographical environment are calculated in terms of national and regional wealth, which includes an assessment of available natural resources and produced and human capitals. The value of national wealth is divided into discrete, persistent and continuously positively changing parts, characterizing the geographical environment. Using the mathematical apparatus, the theoretical problem of how sustainable development is possible in the implementation of contradictory trends in nature conservation, rates of economic growth and social development, is solved. The current national wealth accumulation is described by a weighted sum of independent time functions, which are partial solutions of a linear differential equation with additive control. The national wealth growth functions take into account the accumulated rents for investments in improving the natural environment, in production and creativity. Taking into consideration the share of participation of each component in the national wealth increment, the article proposes a classification of countries and regions in areal coordinates. The sovereign and self-sufficient state of the national wealth of Russia and its regions is characterized by a harmonious (with respect to the set of assets) middle position in the classification, which determines its connecting role in the organization of the world economy to ensure sustainable development. Its mathematical model describes the national wealth accumulation from different income sources and allows comparing the real and calculated trends of long-term changes in the geographical environment of sustainable development using the example of the Russian Federation and the United States of America. New opportunities are opening up for applying mathematical tools to explain the contradictory qualities of sustainable development in different countries, taking into account the uniqueness of the geographical environment in its expanded understanding.
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