Zhuravka A. Modelling of competitional-coopertive interaction in the social-economics systems

The object of research are the nonlinear processes of competitive and cooperative interactions. The aim of this work is the elaboration of the complex of economics-mathematics models of competitive-cooperative interaction, the usage of which will be provide the increase of efficiency of management of social-economic systems. The works of both home and foreign scientists in the field of modelling of social-economic systems and economic dynamics were the methodological basis of this research. In the thesis (dissertation) the tools of systematic analysis, imitation modelling, social-economical forecasting are used. Besides the complex of models of competitive-cooperative interaction based on the provisions of economic theory, the theory of nonlinear dynamic systems and the theory of taking decisions are developed. The scientific importance of the acquired results is analysis and practical application of mathematical models of competitional-cooperative interaction in the social-economical systems. The complex of such models is based on the principles of the balanced and systematic (the aspect of interaction) approaches and the analogy from population dynamics as well. As supplements of the above - mentioned complex of models on the basis of the statistic materials of State Committee of Statistics of Ukraine, a number of applied problems of forecasting and management of innovation invested process (on the example of special regime of investing activity of Kharkov), the market of labour and capital (dynamic of Gross Domestic Product, employed and unemployed population and dynamics requirement of enterprises in workers for filling the vacancies (vacant places) are constructed. It is shown that the suggested complex of competitional cooperative interactions is an analytical instrument for forecasting and management of social-economics systems in which the essential part is played by the process of competition and cooperation.The usage of gravitation model for estimation of intensivity of business activity Ukrainian-Russian-Byelorussian border regions and the balance dynamic Leontiev's model for investigation innovative-branched dynamics of Kharkov region is grounded within the framework of models regional analysis. The calculation on the model has shown that the investments in the branches belonged to innovative-industrial cycle provides the stable growth in the rest branches. The practical significance of the thesis is solving the problems in the field of analysis the labour market of innovative environment and concerted interactions of territory formations. The introducing of the results of the research will enable to increase the efficiency of management of social-economical systems. The stated practical value is of great importance in the branch and the received results of the research are ready for usage.