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

In this work, we investigate the existence of nonmonotone traveling wave solutions to a reaction-diffusion system modeling social outbursts, such as rioting activity, originally proposed in Berestycki et al (Netw Heterog Media. 2015;10(3):443–475). The model consists two scalar values, level unrest and tension field . A key component is bandwagon effect unrest, provided sufficiently high. We focus on so-called tension-inhibitive regime, characterized by fact that has negative feedback tension. This regime been shown be physically relevant for spatiotemporal spread 2005 French riots. use Geometric Singular Perturbation Theory study situations. first when both diffuse at very small rate. Here, time scale over which observed plays role. second case consider diffuses much slower rate than unrest. case, are able deduce driving dynamics modeled well-known Fisher–Kolmogorov-Petrovsky-Piskunov (KPP) equation.