Mathematical Models, Algorithms and Software Package for the National Security State of Russia

  • Natalya YandybaevaEmail author
  • Alexander Rezchikov
  • Vadim Kushnikov
  • Vladimir Ivaschenko
  • Oleg Kushnikov
  • Anatoly Tsvirkun
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)


Mathematical model to determine and predict the main characteristics of the national security of the Russian Federation is developed in the article. A system-dynamic approach is used to develop a predictive mathematical model. To characterize the state of national security the Decree of the President of the Russian Federation identifies the main indicators of national security: citizens ‘satisfaction with the degree of protection of their constitutional rights and freedoms (expert evaluation of sociological surveys); the share of modern weapons, military and special equipment in the Armed Forces of the Russian Federation (% of modern funds in the existing weapons park in the Russian Federation); life expectancy at birth (years); gross domestic product per capita (RUB.); decile coefficient; inflation rate (%)-average annual growth of prices in the country; unemployment rate (%); share of expenditures in gross domestic product for the development of science, technology and education (%); share of expenditures in gross domestic product for culture (%); share of the territory of the Russian Federation that does not meet environmental standards (%). The heuristic algorithm is offered and the computer program for modeling and forecasting of the main characteristics of national security is formed. The results of computational experiments with the developed model, algorithm and software are presented. The method of application for the developed mathematical software for the system of supporting of management decision-making is presented. On ILC the main stages of decision-making to analyze the state of national security of the country at different time intervals using the calculated values of the characteristics of national security are shown. Mathematical software presented in the article is used to analyze the state of the national security of the country and to predict the main indicators of national security of Russia.


National security System dynamics model Differential equations Mathematical model Object-oriented programming 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Balakovo BranchRussian Presidential Academy of National Economy and Public AdministrationBalakovoRussia
  2. 2.Institute of Precision Mechanics and ControlRussian Academy of SciencesSaratovRussia
  3. 3.Yuri Gagarin State Technical UniversitySaratovRussia
  4. 4.Institute of Control ProblemsRussian Academy of ScienceMoscowRussia

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