Mathematical model for forecasting of indicators of economic safety of the Russian Federation

The main characteristics of the state of economic security are the following: the level of unemployment, the decile coefficient, the growth rate of consumer prices, the level of public ex-ternal and domestic debt (% of gross domestic product), the level of health, culture, science and education resources (% of gross domestic product), the level of the annual renewal of weapons, military and special equipment and the level of security and military engineers. A complex of the mathematical models that helps realize simulation and prognostication of the indicators of the Russian Federation national security is developed. The mathematical model based on the system dynamics models, allows formalizing the complex casual relationships between the system variables. The system dynamics model consists of the following elements: the system levels, which represent the reserves (accumulation) in the feedback chains; the streams conveying the content of one level to another; the decision-making procedures that govern the rate of flow between the levels; the information channels connecting the procedures of decisions and the levels. To describe the developed model, the apparatus of ordinary differential equations is used. The indicators of national security are presented as the systemic levels. To illustrate the casual relationships between the system levels, in the developed mathematical model the graph model is used. The regression models are used to verify the adequacy of the system dynamics models. An algorithm for determination of the indicators of national security while solving a number of nonlinear differential equations is proposed. The practical implementation of the developed mathematical models is shown, and the predictive values of the indicators of national security, calculated by the system dynamics models and the regression model, are compared.