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

For citation:

Kurkina E. S., Kuretova E. D. Mathematical models of the world-system evolution. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 6, pp. 88-107. DOI: 10.18500/0869-6632-2013-21-6-88-107

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 241)
Article type: 

Mathematical models of the world-system evolution

Kurkina Elena Sergeevna, Lomonosov Moscow State University
Kuretova Ekaterina Dmitrievna, Lomonosov Moscow State University

We propose new mathematical models of the evolution of the human society based on the synergistic approach. They describe the dynamics of the indicators of the major integral development of the World-System such as the total population and the level of the technological development. Our models capture the basic laws of the space and temporal development of the society. They indicate the hyperbolic growth of the population that agrees with the demographical data and the cyclic dynamics. The models help to analyze historical events and to make some predictions fro the further development of the society.

  1. Grinin LE, Korotaev AV. Social macroevolution: genesis and transformations of the World-System. Moscow: Librokom, URSS, 2009. 568 p. (In Russian).
  2. Kapitza SP. Essay About The Theory Of Growth Of Humanity. Demography Revolution And Information Society. Moscow: MMVB; 2008. (In Russian).
  3. Kapitsa SP. Demographic revolution, global security and the future of humanity. Russia's future is in the mirror of synergy. Moscow: KomKniga; 2006. 238–254 p. (In Russian).
  4. Korotaev AV, Malkov AS, Khalturina DA. The laws of history. Mathematical modeling of historical macroprocesses. Demographics, economics, wars. Moscow: KomKniga; 2005. 344 p. (In Russian).
  5. Nefedov SA. Factor analysis of the historical process. History and mathematics. Conceptual space and search directions. Moscow: LKI; 2008. 63–87 p. (In Russian).
  6. Dyakonov IM. History paths. From the oldest man to the present day. Moscow: Vostlit; 1994. 382 p. (In Russian).
  7. Yakovets YuV. Cycles. Crises. Forecasts. Мoscow: Nauka; 1999. 448 p. (In Russian).
  8. Akaev AA. Fundamentals of modern theory of innovation and technological development of the economy and management of the innovation process. Analysis and simulation of global dynamics. Мoscow: Librokom; 2010. 17–43 p. (In Russian).
  9. Rodoman BB. Territorial ranges and networks. Smolensk: Oikumena; 1999. 256 p. (In Russian).
  10. Grinin LE, Korotaev AV. Model of economic and demographic development World-Systems of Artsruni-Komlos and theory of production revolutions. Analysis and models. global dynamics. Moscow: Librium; 2010. 143–185 p. (In Russian).
  11. Kurdyumov VS. Regimes with exacerbation: The evolution of the idea. Ed. Malinetsky GG. Moscow: Fizmatlit; 2006. 308 p. (In Russian).
  12. Belavin VA, Kapitza SP, Kurdyumov SP. A mathematical model of global demographic processes with regard to the spatial distribution. Zh. Vychisl. Mat. Mat. Fiz. Comput. Math. Math. Phys. 1998;38(6):849–865.
  13. Belavin VA, Knyazeva EN, Kurkina EU. Mathematical modeling of global dynamics of the world community. Nonlinearity in modern natural science. Moscow: Librikom; 2009. 384–408 p.
  14. Knyazev EN, Kurkina EU. Ways of history and images of the future of mankind: Synergy of global processes in history. Philosophy and Culture. 2008;10(10):28–49.
  15. Knyazev EN, Kurkina EU. Global dynamics of the global community. Historical Psychology & Sociology. 2009;2(1):129–153.
  16. Kurkina ES. Mathematical modeling of the global evolution of the world community. Demographic explosion and collapse of civilization. History and mathematics. Analysis and simulation of global dynamics. Moscow: Librikom; 2010. 2307 p. (In Russian).
  17. Kuretova ED, Kurkina ES. Modeling general laws of spatial-temporal evolution grows and historical cyclesю Computational Mathematics and Modeling. New York: Springer. 2010;21(2):70–89. DOI: 10.1007/s10598-010-9055-9.
  18. Kurdyumov SP, Kurkina ES, Telkovskaya OV. Regimes with sharpening in two-component media. Matem. Mod. 1989;1(1):34–50.
Short text (in English):
(downloads: 111)