Formation and suppression of hotspots in urban crime models with law enforcement.

Abstract

We analyze a system of partial differential equations introduced as a model for urban crime with law enforcement. This system is known to obtain spatially localized patterns representing crime hotspots. In this work, we obtain the amplitude equations that describe the hotspot pattern formation in the model using weakly nonlinear analysis techniques. In particular, we find the existence of super- and sub-critical pitchfork bifurcations. Moreover, we propose different suppression strategies and investigate numerically how the suggested approaches effectively eradicate the two types of hotspots. We highlight the challenges in weakly nonlinear analysis and the limitations of the proposed suppression mechanisms, emphasizing the need for further theoretical and practical work on this urban crime model with law enforcement.