A model of riots dynamics: shocks, diffusion and thresholds (Q258503)

The present paper deals with some mathematical models involving riots dynamics. After reviewing some concrete rioting activities from the past (in particular in France, in the USA and in the UK), the authors aim to construct valid models that describe the dynamics of these events.NEWLINENEWLINEThe studied PDE systems involve the coupling of an explicit variable describing the \textit{intensity of rioting activities} and an underlying (implicit) field of \textit{social tension}. The models try to qualitatively capture the initiation, self-excitation, spreading and relaxation of rioting activities. These models are considered either on networks or in a spatially continuous setting. The authors analyze the existence of \textit{traveling wave} and \textit{spreading} type solutions and they also present the numerical analysis of some of the systems.NEWLINENEWLINEIn addition to the obtained results, several new open mathematical problems are formulated on the systems.