Key words
system dynamics, mathematical model, national security indicators, differential equations, the theory of chaos
articles
Authors:
Rezchikov A., Bogomolov A., Filimonyuk L., Ivaschenko V., Kushnikov V., Yandybaeva N. Published in
№ 2(68)
29 april 2017 year
Rubric: Models and Methods
Rubric: Models and Methods
Model to assess the state of Russia’s national security, based on system dynamics theory
Actual today is the development of mathematical models for simulation experiments to ensure the
country’s transition to sustainable development. The main indicators of national security, according to
Presidential Decree № 683 «National Security Strategy of the Russian Federation» are: satisfaction of citizen
of degree of protection of their constitutional rights and freedoms, personal and property interests,
including from criminal encroachments; the share of modern weapons, military and special equipment
in the Russian Armed Forces; the life expectancy; gross domestic product per capita; inflation; the share
of expenditure in the gross domestic product for culture, as well as the development of science, technology
and education; the part of the territory of the Russian Federation, that do not meet environmental
standards. Developed a complex of mathematical models for modeling and the prognostication indicators
of Russia’s national security. Mathematical model developed based on system dynamics models,
allows formalizing the complex casual relationships between system variables. System dynamics model
consists of the following elements: the system levels (the simulated variables), which represent the accumulation
of (accumulation) in feedback circuits; streams conveying the content of one level to another;
making procedures that govern the rate of flow between the levels; information channels connecting procedures
decisions levels. To describe the model developed using the apparatus of ordinary differential
equations. As systemic levels presented the indicators of national security. To illustrate the casual relationships
between system-level mathematical model developed using the graph model. Regression models
are used to verify the adequacy of system dynamics models. An algorithm is proposed for determining
of indicators of national security for solves the system of nonlinear differential equations. Shows the
practical implementation of the mathematical support developed and compared predictive values of indicators
of national security. Performed modeling of chaotic phenomena in the Russian economy in 1994.
The author:
Rezchikov A.
Degree:
Dr of Technique, Professor, Corresponding Member of the Russian Academy of Sciences, Institute of Precision M echanics and Control, Russian Academy of Sciences
Location:
Saratov
All articles:
The author:
Bogomolov A.
Degree:
PhD of Physics & Mathematics, Associate Professor, Institute of Precision Mechanics and Control, Russian Academy of Sciences
Location:
Saratov
All articles:
The author:
Filimonyuk L.
Degree:
PhD in Technique, Institute of Precision Mechanics and Control, Russian Academy of Sciences
Location:
Saratov
All articles:
The author:
Ivaschenko V.
Degree:
Dr of Engineering, Professor, Academic Secretary, Institute of Precision Mechanics and Control, Russian Academy of Sciences
Location:
Saratov
All articles:
The author:
Kushnikov V.
Degree:
Dr of Technique, Professor, Institute of Precision Mechanics and Control, Russian Academy of Sciences
Location:
Saratov
All articles:
The author:
Yandybaeva N.
Degree:
PhD in Technique, Associate Professor of department of information and documentation management, Balakovo branch of the Russian academy of national economy and public administration under the President of the Russian Federation
Location:
Balakovo
