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Dynamic variant of mathematical model of collective behavior

Systems Analysis and Operations Research

Abstract

In 2014, P.S. Krasnoshchekov, Academician at the Russian Academy of Sciences, offered A.A. Belolipetskii to continue research on the collective behavior of people by generalizing his earlier static model to the dynamic case. For this reason, this work is regarded as a tribute to commemorate Krasnoschekov, an outstanding scientist. The fundamental quantitative model Krasnoshchekov proposed in his works studied a static model of collective behavior when people can change their original opinion on a subject after one stage of informational interaction. Opinions are assumed to be alternatives. A person can support his country to join the WTO with probability p and object to it with probability 1 - p. In this work, multistep opinion exchange processes are considered. Quantitative characteristics of values of probabilities p (of people’s opinions) are obtained as functions of the step number and the rate of change of these probabilities. For instance, the way the mass media can control the opinions of their target audience if this audience has certain psychological characteristics is studied.

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References

  1. 1.
    P. S. Krasnoshchekov, “The simplest mathematical model of behaviour. Psychology of conformism,” Mat. Model. 10 (7), 76–92 (1998).Google Scholar
  2. 2.
    P. S. Krasnoshchekov and A. A. Petrov, Principles of Model Construction (Fazis, VTs RAN, Moscow, 2000) [in Russian].MATHGoogle Scholar
  3. 3.
    A. A. Vasin, P. S. Krasnoshchekov, and V. V. Morozov, Study of Operations. Applied Mathematics and Informatics (Akademiya, Moscow, 2008) [in Russian].Google Scholar
  4. 4.
    T. C. Schelling, The Strategy of Conflict (Harvard Univ. Press, Boston, 1980).MATHGoogle Scholar
  5. 5.
    A. Banerjee and T. Besley, “Peer group externalities and learning incentives: a theory of nerd behavior,” J. M. Olin Discussion Paper No. 68 (Dep. Economics, Woodrow Wilson School of Public Int. Affairs, Princeton Univ. Press, Princeton, 1990).Google Scholar
  6. 6.
    D. Helbing, I. Farkas, P. Molnar, and T. Vicsek, “Simulation of pedestrian crowds in normal and evacuation situations,” Pedestr. Evacuat. Dyn. 21 (2), 21–58 (2002).Google Scholar
  7. 7.
    M. E. Stepantsov, “Mathematical model for the directed motion of a people group,” Mat. Model. 16 (3), 43–49 (2004).MathSciNetMATHGoogle Scholar
  8. 8.
    E. S. Kirik, D. V. Kruglov, and T. B. Yurgel’yan, “On discrete people movement model with environment analysis,” Zh. Sib. Fed. Univ., Ser. Mat. Fiz. 1 (3), 262–271 (2008).Google Scholar
  9. 9.
    V. V. Breer, “Conformal behavior models. Part 1. From philosophy to math models,” Probl. Upravl. 11 (1), 2–13 (2014).Google Scholar
  10. 10.
    P. P. Makagonov, S. B. R. Espinosa, and K. A. Lutsenko, “Algorithm for expert influence calculation on information consumer in social networks and educational sites,” Model. Analiz Dannykh, No. 1, 74–85 (2014).Google Scholar
  11. 11.
    A. A. Belolipetskii and I. V. Kozitsin, “On one mathematical model of collective behavior in differential form,” in Mathematical Simulation of Information Systems (Mosk. Fiz. Tekh. Inst., Moscow, 2015), pp. 66–73 [in Russian].Google Scholar
  12. 12.
    A. L. Beklaryan, “Exit front in the model of crowd’s behavior in extreme situations,” Vestn. Tambov. Univ., Ser.: Estestv. Tekh. Nauki 20 (5), 11–23 (2015).Google Scholar
  13. 13.
    F. R. Gantmakher, Matrix Theory (Nauka, Fizmatlit, Moscow, 1967; Chelsea, New York, 1960).Google Scholar
  14. 14.
    S. A. Ashmanov, Introduction to Mathematical Economics (Moscow, Nauka, 1984) [in Russian].MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Institute of Control Sciences of the Russian Academy of SciencesMoscowRussia

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