  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.
