Christina Wang, Department of Applied Mathematics, University of Colorado Boulder

Traveling Wave Solutions of a Reaction-Diffusion System Modeling Social Outbursts

Despite legal recognition of protest activity, the historical interaction between the government and protesters has been complex. Motivated by the "wave-like” dynamics of rioting activity during the French riots in 2005, a system of equations is introduced to model the interplay between the dynamics of protesters, social tension, and law enforcement. We establish the existence and stability of traveling wave solutions in this system, supported by both theoretical analyses and numerical simulations. Changes in certain parameters cause a qualitative difference in the solution to the system, leading to situations that correspond to different protest management strategies. We delve into the impact of two distinct protest management approaches on the qualitative and semi-quantitative characteristics of the traveling waves.