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Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach

Author

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  • Sergei Petrovskii

    (School of Mathematics and Actuarial Science, University of Leicester, Leicester LE1 7RH, UK
    Peoples Friendship University of Russia (RUDN), 6 Miklukho-Maklaya St, Moscow 117198, Russia)

  • Weam Alharbi

    (Mathematics Department, Faculty of Science, Tabuk University, Tabuk 71491, Saudi Arabia)

  • Abdulqader Alhomairi

    (Department of Curriculum and Teaching Methods, Faculty of Education and Art, Tabuk University, Tabuk 71491, Saudi Arabia)

  • Andrew Morozov

    (School of Mathematics and Actuarial Science, University of Leicester, Leicester LE1 7RH, UK
    Institute of Ecology and Evolution, Russian Academy of Sciences, 33 Leninskii pr., Moscow 119071, Russia)

Abstract

Understanding of the dynamics of riots, protests, and social unrest more generally is important in order to ensure a stable, sustainable development of various social groups, as well as the society as a whole. Mathematical models of social dynamics have been increasingly recognized as a powerful research tool to facilitate the progress in this field. However, the question as to what should be an adequate mathematical framework to describe the corresponding social processes is largely open. In particular, a great majority of the previous studies dealt with non-spatial or spatially implicit systems, but the literature dealing with spatial systems remains meagre. Meanwhile, in many cases, the dynamics of social protests has a clear spatial aspect. In this paper, we attempt to close this gap partially by considering a spatial extension of a few recently developed models of social protests. We show that even a straightforward spatial extension immediately bring new dynamical behaviours, in particular predicting a new scenario of the protests’ termination.

Suggested Citation

  • Sergei Petrovskii & Weam Alharbi & Abdulqader Alhomairi & Andrew Morozov, 2020. "Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach," Mathematics, MDPI, vol. 8(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:78-:d:304768
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    References listed on IDEAS

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    1. Maria Fonoberova & Vladimir A. Fonoberov & Igor Mezic & Jadranka Mezic & P. Jeffrey Brantingham, 2012. "Nonlinear Dynamics of Crime and Violence in Urban Settings," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(1), pages 1-2.
    2. Lang, J.C. & De Sterck, H., 2014. "The Arab Spring: A simple compartmental model for the dynamics of a revolution," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 12-21.
    3. Dan Braha, 2012. "Global Civil Unrest: Contagion, Self-Organization, and Prediction," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-9, October.
    4. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
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    1. Inferrera, G. & Munafò, C.F. & Oliveri, F. & Rogolino, P., 2024. "Reaction-diffusion models of crimo–taxis in a street," Applied Mathematics and Computation, Elsevier, vol. 467(C).

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