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Theoretical Study of Self-organized Phase Transitions in Microblogging Social Networks

  • Andrey Dmitriev
  • Svetlana Maltseva
  • Olga Tsukanova
  • Victor Dmitriev
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 813)

Abstract

A simple sociophysical model is proposed to describe the transition between a chaotic and a coherent state of a microblogging social network. The model is based on the equations of evolution of the order parameter, the conjugated field, and the control parameter. The self-consistent evolution of the networks is presented by equations in which the correlation function between the incoming information and the subsequent change of the number of microposts plays the role of the order parameter; the conjugate field is equal to the existing information; and the control parameter is given by the number of strategically oriented users. Analysis of the adiabatic approximation shows that the second-order phase transition, which means following a definite strategy by the network users, occurs when their initial number exceeds a critical value equal to the geometric mean of the total and critical number of users.

Notes

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (grant 16-07-01027).

References

  1. 1.
    Savoiu, G.: Econophysics. Background and Applications in Economics, Finance, and Sociophysics. Elsevier, Amsterdam (2013)Google Scholar
  2. 2.
    Schweitzer, F.: Sociophysics. Phys. Today 71, 41–46 (2018)CrossRefGoogle Scholar
  3. 3.
    Price, D.: Networks of scientific papers. Science 149, 510–515 (1965)CrossRefGoogle Scholar
  4. 4.
    Barabasi, A.-L., Rreka, A.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Barabasi, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47 (2002)Google Scholar
  6. 6.
    Tadic, B., Dankulov, M., Melnikc, R.: Mechanisms of self-organized criticality in social processes of knowledge creation. Phys. Rev. E 96, 032307 (2017)Google Scholar
  7. 7.
    Tadic, B., Gligorijevic, V., Mitrovic, M., Suvakov, M.: Co-evolutionary mechanisms of emotional bursts in online social dynamics and networks. Entropy 15, 5084–5120 (2013)CrossRefGoogle Scholar
  8. 8.
    Butts, C.T.: The complexity of social networks: theoretical and empirical findings. Soc. Netw. 23, 31–72 (2001)CrossRefGoogle Scholar
  9. 9.
    Skvoretz, J.: Complexity theory and models for social networks. Complexity 8, 47–55 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Everett, M.G.: Role similarity and complexity in social networks. Soc. Netw. 7, 353–359 (1985)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ebel, H., Davidsen, J., Bornholdt, S.: Dynamics of social networks. Complexity 8, 24–27 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bocaletti, S., Latora, V., Moreno, Y., Hwang, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F. Critical phenomena in complex networks. Rev. Mod. Phys. 80, 1275 (2008)Google Scholar
  14. 14.
    Fronczak, P., Fronczak, A., Holyst, J.A.: Phase transitions in social networks. Eur. Phys. 59, 133–139 (2007)CrossRefGoogle Scholar
  15. 15.
    Li, L., Scaglione, A, Swami, A., Zhao, Q.: Phase transition in opinion diffusion in social networks. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3073–3076 (2012)Google Scholar
  16. 16.
    Floria, L.M., Gracia-Lazaro, C., Moreno, Y.: Social network reciprocity as a phase transition in evolutionary cooperation. Phys. Rev. E 79, (2009)Google Scholar
  17. 17.
    Perc, M.: Phase transitions in model of human cooperation. Phys. Lett. A 380, 2803–2808 (2016)CrossRefGoogle Scholar
  18. 18.
    Clark, L.W., Feng, L., Chin, C.: Universal soace-time scaling symmetry in the dynamics of bosons across a quantum phase transition. Science 354, 606–610 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Olemskoi, A.I., Khomenko, A.V., Kharchenko, D.O.: Self-organized criticality within fractional Lorenz scheme. Phys. A 323, 263–293 (2003)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Olemskoi, A.I., Kharchenko, D.O.: Kinetics of phase transitions with singular multiplicative noise. Phys. Solid State 42, 532–538 (2000)CrossRefGoogle Scholar
  21. 21.
    Olemskoi, A.I., Khomenko, A.V.: Three-parameter kinetics of a phase transition. J. Theor. Exp. Phys. 81, 1180–1192 (1996)Google Scholar
  22. 22.
    Olemskoi, A.I., Khomenko, A.V., Knyaz, A.I.: Phase transitions induced by noise cross-correlations. Phys. Rev. E 71, 041101 (2005)Google Scholar
  23. 23.
    Pogrebnjak, A.D., Bagdasaryan, A.A., Pshyk, A., Dyadyura, K.: Adaptive multicomponentnanocomposite coatings in surface engineering. Phys. Uspekhi 60, 586–607 (2017)CrossRefGoogle Scholar
  24. 24.
    Uddin, M.M., Imran, M., Sajjad, H.: Understanding Types of Users on Twitter. In: 6th ASE International Conference in Social Computing (2014)Google Scholar
  25. 25.
    Atkins, P.W.: The elements of physical chemistry. Oxford University Press, Oxford (1993)Google Scholar
  26. 26.
    Risken, H.: The Fokker–Planck Equation: Methods of Solutions and Applications. Springer, Berlin (1984)Google Scholar
  27. 27.
    Bouchaud, J.P., Georges, A.: Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127–293 (1990)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Tsukanova, O.A., Vishnyakova, E.P., Maltseva, S.V.: Model-based monitoring and analysis of the network community dynamics in a textured state space. In: 16th IEEE Conference on Business Informatics, pp. 44–49 (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Andrey Dmitriev
    • 1
  • Svetlana Maltseva
    • 1
  • Olga Tsukanova
    • 1
  • Victor Dmitriev
    • 1
  1. 1.National Research University Higher School of EconomicsMoscowRussia

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