Analysis of a model for the dynamics of riots

TL;DR

This paper models the dynamics of riots and social upheaval waves, analyzing how information restriction and environmental heterogeneities influence riot activity and wave propagation.

Contribution

It extends previous models by incorporating information restriction effects and heterogeneities, proving existence of solutions and exploring wave behaviors through simulations.

Findings

Existence of global solutions to the model.

Traveling wave solutions under certain conditions.

Heterogeneities induce pulsating wave patterns.

Abstract

This paper is concerned with modeling the dynamics of social outbursts of activity, such as protests or rioting activity. In this sequel to our work in \cite{Berestycki2014}, written in collaboration with J-P. Nadal, we model the effect of restriction of information and explore the effects that it has on the existence of {\it upheaval waves}. The systems involve the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. We prove the existence of global solutions to the Cauchy problem in $\mathbb{R}^d$ as well as the existence of {\it traveling wave solutions} under certain parameter regimes. We furthermore explore the effects of heterogeneities in the environment with the help of numerical simulations, which leads to pulsating waves in certain cases. We analyze the effects of periodic domains as well as the {\it barrier} problem with the help of numerical simulations and discuss many open problems.