On the Possibility of Developing a Dynamic Model of Social and Economic System Management
The aim of the study is to select and substantiate the conditions for the system integration of the properties of social, economic and technical-technological systems, expressed in the model of interaction of their basic indicators. The main hypothesis of the study is the existence of a stable connection between three systems: social, economic and technical and technological. The following questions were addressed: the main modern trends in the development of social and economic systems were considered; a mathematical model of the interaction of three basic indicators describing the state of social, economic, technical and technological systems was formed; the rationale for the choice of the three basic components of the model with consideration of the nature of their interaction was given; on the basis of the selected basic components, a system of three differential equations was formed that describe the interaction of indicators of the population size, the number of jobs and the supply of the system with energy; the composition is determined and the value of the coefficients providing the relationship of the basic indicators of the model is explained. Various solutions to the presented system of three differential equations were also obtained. The graphs of solutions corresponding to the stability criterion of Lyapunov dynamical systems are presented. The fundamental possibility of using the objective criterion of Lyapunov stability to study the possibilities of social and economic systems to sustainably reproduce themselves in time is noted. The advantages of the proposed approach to modeling the process of development of social and economic systems are considered. The main limitations of the proposed model and the disadvantages of the proposed approach are highlighted. The tasks are set for further research of the capabilities of the formed mathematical model. The main scientific methods used were the decomposition method, the aggregation method, the mathematical modeling method.