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Open AccessArticle

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

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
Mathematics Department, Faculty of Science, Tabuk University, Tabuk 71491, Saudi Arabia
Department of Curriculum and Teaching Methods, Faculty of Education and Art, Tabuk University, Tabuk 71491, Saudi Arabia
Institute of Ecology and Evolution, Russian Academy of Sciences, 33 Leninskii pr., Moscow 119071, Russia
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 78;
Received: 1 November 2019 / Revised: 13 December 2019 / Accepted: 20 December 2019 / Published: 3 January 2020
(This article belongs to the Special Issue Partial Differential Equations in Ecology: 80 Years and Counting)
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. View Full-Text
Keywords: social dynamics; wave of protests; long transients; ghost attractor social dynamics; wave of protests; long transients; ghost attractor
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Petrovskii, S.; Alharbi, W.; Alhomairi, A.; Morozov, A. Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach. Mathematics 2020, 8, 78.

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