Economic-mathematical Models for Analyzing the Potential for Self-Development of Territorial Systems

The article is devoted to the construction of tools to support decision-making for the analysis and formation of conditions for self-development of administrative-territorial entities, which contributes to the creation of a competitive environment in them. The Toolkit is based on the use of methods of economic and mathematical modeling in the selection of methods of inter-budgetary regulation in the aspect of activation of functions: stimulating and leveling. The incentive function is aimed at increasing the motivation of the authorities in building up the territorial tax potential and is implemented through the distribution of tax revenues among the budgets vertically according to established standards. The leveling function is performed through financial assistance methods. In order to support decision-making regarding the application of forms of financial policy, the article offers a mathematical model for analyzing territorial units from the point of view of identifying the potential for self-development of territories. The model is based on the application of nonlinear dynamics methods that allow us to get an idea of the qualitative picture of the trend in the dynamics of indicators of development of the territorial system. The presence of an attractor in the dynamics of indicators allows us to judge the potential ability of the territory to self-organization and determines the feasibility of using the stimulating function of inter-budgetary regulation as a prerequisite for the sustainable development of the socio-economic system at the expense of its own revenue sources.