A numerical perspective on traveling wave solutions in a system for rioting activity

摘要

Motivated by the “wave-like” dynamics of rioting activity that occurred during the 2005 French riots we analyze numerically the existence and qualitative properties of traveling wave solutions to a system of reaction-diffusion equations which was proposed to model the spatio-temporal dynamics of rioting activity and social tension in [6]. With the use of AUTO and Matlab we classify the various regions separating the number of homogeneous steady-states solutions and analyze their stability, which turns out to be very rich. We discover a zoology of traveling wave solutions displaying a variety of interesting characteristics. Through this analysis we can make conclusions about the factors leading to different characteristics which have been observed in different riots. For example, the analysis provides evidence that the 2005 French riots were tension-inhibitive (where rioting helps release tension) versus tension-enhansing (where rioting slows down the release of tension).