ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Petukhov A. Y. Development of the Russian state in the 20th and 21st centuries: Mathematical modeling based on the socio-energy approach. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 3, pp. 365-375. DOI: 10.18500/0869-6632-2021-29-3-365-375

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 782)
Article type: 

Development of the Russian state in the 20th and 21st centuries: Mathematical modeling based on the socio-energy approach

Petukhov Aleksandr Y, Lobachevsky State University of Nizhny Novgorod

Purpose. The article is devoted to modeling the socio-political development of Russia in 1910–2009 based on the author’s socio-energy approach. In this paper, we briefly talk about the basics of the proposed approach, its principles and basic equations. Methods. The mathematical model is based on the Langevin diffusion equation. We also introduce the concepts of social energy, coefficients of the state of society and give them definitions. Results. Based on its, computer modeling is carried out and the characteristic regularity of the development of society in Russia in 1910–2009 is derived. Conclusion. We can notice the spiral pattern of the Russian society in the 20th century. Depending on the density, scale and diversity of events «the flow» of history is accelerating, and the movement in the coil becomes «faster». On its basis, the further development of the Russian society and the state as a whole can be predicted.

  1. Plotinsky YM. Models of Social Processes. Textbook for Higher Educational Institutions. Moscow: Logos; 2001. 296 p. (in Russian).
  2. Malkov SY. Mathematical Modeling of Historical Trends. Approaches and Processes. Moscow: RSSU; 2004. P. 76–188 (in Russian).
  3. Ebeling W. Strukturbildung bei irreversiblen Prozessen: Eine Einfuhrung in die Theorie dissipativer ¨ Strukturen. Aufl. 1. Bd. 60. Leipzig: Teubner-Verlag; 1976. 194 s. (in German).
  4. Haggett P. Locational Analysis in Human Geography. Arnold; 1965. 339 p.
  5. Armand AD, Lyuri DI, Zherikhin VV, Rautian AS, Kaidanova OV, Kozlova EV, Streletsky VN, Budanov VG. Anatomy of Crises. Moscow: Nauka; 1999. 238 p. (in Russian).
  6. Romanovsky YM, Stepanova NV, Chernavskii DS. Mathematical Biophysics. Moscow: Nauka; 1984. 304 p. (in Russian).
  7. Melik-Gaykazyan IV. Information Processes and Reality. Moscow: FIZMATLIT; 1997. 192 p. (in Russian).
  8. Haken H. Advanced Synergetics. Instability Hierarchies of Self-Organizing Systems and Devices. Vol. 20 of Springer Series in Synergetics. Springer-Verlag Berlin Heidelberg; 1983. 356 p. DOI: 10.1007/978-3-642-45553-7.
  9. Nicolis G, Prigogine I. Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations. J. Wiley & Sons, New York, London, Sydney, Toronto; 1977. 491 p.
  10. Malinetskii GG, Potapov AB. Modern Problems of Nonlinear Dynamics. Moscow: Editorial URSS; 2000. 336 p. (in Russian).
  11. Malinetskii GG. Chaos, Structures, Computational Experiment. Introduction to Nonlinear Dynamics. Moscow: Editorial URSS; 2002. 256 p. (in Russian).
  12. Ho lyst JA, Kacperski K, Schweitzer F. Phase transitions in social impact models of opinion formation. Physica A. 2000;285(1–2):199–210. DOI: 10.1016/S0378-4371(00)00282-X.
  13. Loskutov AY, Mikhailov AS. Introduction to Synergetics. Moscow: Nauka; 1990. 272 p. (in Russian).
  14. Dmitriev AS, Starkov SO, Shirokov ME. Synchronization of ensembles of coupled maps. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(4–5):40–58 (in Russian).
  15. New in Synergetics. Mysteries of the World of Nonequilibrium Structures. Ed. I.M. Makarov. Moscow: Science; 1996. 263 p. (in Russian).
  16. Alekseev YK, Sukhorukov AP. Introduction to Catastrophe Theory. Moscow: MSU; 2000. 173 p. (in Russian).
  17. Poston T, Stewart I. Catastrophe Theory and Its Applications. London: Pitman Publishing; 1978. 491 p.
  18. Vladimirov VA, Vorobiev YL, Salov SS, Faleev MI, Arkhipova NI, Kapustin MA, Kashchenko SA, Kosyachenko SA, Kuznetsov IV, Kul’ba VV, Malinetskii GG, Makhutov NA, Pisarenko VF, Podlazov AV, Posashkov SA, Potapov AB, Shnirman MG. Risk Management: Risk. Sustainable Development. Synergetics. Moscow: Nauka; 2000. 431 p. (in Russian).
  19. Podlazov AV. The paradigm of self-organized criticality. Keldysh Institute Preprints. 1995:086 (in Russian).
  20. Moon F. Chaotic Vibrations: An Introduction For Applied Scientists And Engineers. Somerset, New Jersey, USA: J. Wiley & Sons; 1987.
  21. Petukhov AY, Malhanov AO, Sandalov VM, Petukhov YV. Mathematical modeling of ethnosocial conflicts with the introduction of the control function. Simulation. 2020;96(3):337–346. DOI: 10.1177/0037549719884629.
  22. Smirnov AV. State, society, justice: energy approach and the right philosophy. Philosophy and Law. Proceedings of the International Scientific-Practical Conference. February 28, 2006. St. Petersburg: SPbUHSS; 2006. P. 108–110 (in Russian).
  23. Volkova VN, Denisov AA. Basics of Systems Theory and Systems Analysis. St. Petersburg: SPbSIT; 1997 (in Russian)