  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.
