A model of riots dynamics: Shocks, diffusion and thresholds

Henri  Berestycki; Jean-Pierre  Nadal; Nancy  Rodíguez; Henri  Berestycki; Jean-Pierre  Nadal; Nancy  Rodíguez

doi:10.3934/nhm.2015.10.443

Networks and Heterogeneous Media

2015, Volume 10, Issue 3: 443-475. doi: 10.3934/nhm.2015.10.443

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A model of riots dynamics: Shocks, diffusion and thresholds

1.
Ecole des Hautes Etudes en Sciences Sociales and CNRS, Centre d'Analyse et de Mathématique Sociales (CAMS, UMR8557), 190-198, avenue de France - 75013 Paris
2.
Ecole des Hautes Etudes en Sciences Sociales and CNRS, Centre d'Analyse et de Mathématique Sociales (CAMS, UMR8557), 190-198 avenue de France - 75013 Paris
3.
UNC Chapel Hill, Department of Mathematics, Phillips Hall, CB # 3250, Chapel Hill, NC 27599-3250

Received: 01 November 2014 Revised: 01 February 2015
Primary: 35K55, 35K57; Secondary: 35B99.

We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. Our models include the effects of exogenous and endogenous factors as well as various propagation mechanisms. From numerical and mathematical analysis of these models we show that the assumptions made on how different locations influence one another and how the tension in the system disperses play a major role on the qualitative behavior of bursts of social unrest. Furthermore, we analyze here various properties of these systems, such as the existence of traveling wave solutions, and formulate some new open mathematical problems which arise from our work.
- Mathematical modeling,
- partial differential equations,
- traveling wave solutions,
- numerical solutions,
- non-local diffusion
Citation: Henri Berestycki, Jean-Pierre Nadal, Nancy Rodíguez. A model of riots dynamics: Shocks, diffusion and thresholds[J]. Networks and Heterogeneous Media, 2015, 10(3): 443-475. doi: 10.3934/nhm.2015.10.443

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Abstract

We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. Our models include the effects of exogenous and endogenous factors as well as various propagation mechanisms. From numerical and mathematical analysis of these models we show that the assumptions made on how different locations influence one another and how the tension in the system disperses play a major role on the qualitative behavior of bursts of social unrest. Furthermore, we analyze here various properties of these systems, such as the existence of traveling wave solutions, and formulate some new open mathematical problems which arise from our work.

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