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Spatiotemporal patterns of social protests: Reaction–diffusion approach

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  • Morozov, Andrew
  • Manna, Kalyan
  • Banerjee, Malay
  • Petrovskii, Sergei

Abstract

Mathematical modelling of riots and protests is becoming a powerful tool in providing a better understanding of dynamics of social unrest with the ultimate goal to ensure a sustainable development of the human society. Here we explore spatialtemporal patterns of social protests using a reaction–diffusion modelling framework. Our model includes two variables: the number of protesters and the cumulative amount of the damage made as an outcome of the protest. The system has been studied analytically as well as by means of extensive numerical simulation in one dimensional and two-dimensional physical space. The model of protests exhibits a variety of dynamical regimes, including regular and chaotic patterns. In particular, we found an interesting scenario where two chaotic attractors with different spatial structure can co-exist for the same set of model parameters. We reveal the complex structure of the parameter space of the model identifying the range of key parameters for which different dynamical regimes are possible.

Suggested Citation

  • Morozov, Andrew & Manna, Kalyan & Banerjee, Malay & Petrovskii, Sergei, 2026. "Spatiotemporal patterns of social protests: Reaction–diffusion approach," Chaos, Solitons & Fractals, Elsevier, vol. 208(P2).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p2:s0960077926003255
    DOI: 10.1016/j.chaos.2026.118184
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