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This paper is concerned with the methods of mathematical modeling of the socio-economic development of regions. The objective of this study is to analyze and assess the socio-economic potential of the territory having regard to its individual socio-economic and economic-geographical characteristics. The territory's individual characteristics, in turn, are treated as invariant conditions of its development. The study territory includes regions and federal districts of the Russian Federation. An assessment of the regions' development potential is made from the perspective of analyzing their current socio-economic situation for the time interval 1999-2002 taken from official statistical handbooks. To accomplish this, a special-purpose mathematical model is developed in the form of a hierarchical fractal indicative function relating the generalized indicator characterizing the regions' development potential, or the “indicated” (that which is indicated versus indicator), to the particular socio-economic characteristics of the territory, or the development indicators of the local economy, via the model coefficients which is termed regulators. As a result, the economic-mathematical model is generated in the form of an indicative function characterizing the current socio-economic situation of the regions and federal districts of Russia on different levels of economic organization (from local and regional to national). It reflects appropriately and dramatically the specific character of the region's socio-economic potential by the example of the connection of investments with the volumes of production. The model permits the position of the regions and districts to be identified in the system of inter-regional and national socio-economic links and economic-geographical conditions of development. The results derived from modeling the socio-economic development potential of Russia's regions have been used to construct the control surface of the country's economy characterizing the changes in the development potential of the federal districts toward its decrease.

mathematical modelling of natural phenomena

Modeling of the Socio-Economic Potential of the Siberian Regions with Consideration for their Economic-Geographical Position in the National Economic System of the Russian Federation