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In this work we investigate the existence of non-monotone traveling wavesolutions to a reaction-diffusion system modeling social outbursts, such asrioting activity, originally proposed in arXiv:1502.04725v3. The model consistsof two scalar values, the level of unrest $u$ and a tension field $v$. A keycomponent of the model is a bandwagon effect in the unrest, provided thetension is sufficiently high. We focus on the so-called tension inhibitiveregime, characterized by the fact that the level of unrest has a negativefeedback on the tension. This regime has been shown to be physically relevantfor the spatiotemporal spread of the 2005 French riots. We use GeometricSingular Perturbation Theory to study the existence of such solutions in twosituations. The first is when both $u$ and $v$ diffuse at a very small rate.Here, the time scale over which the bandwagon effect is observed plays a keyrole. The second case we consider is when the tension diffuses at a much slowerrate than the level of unrest. In this case, we are able to deduce that thedriving dynamics are modeled by the well-known Fisher-KPP equation.

Traveling wave solutions in a model for social outbursts in a tension-inhibitive regime