Dynamical analysis of a switched social behavior model

Crime is on the rise all around the world. Over many years, researchers have investigated various approaches to create effective systems and strategies that can reduce negative behavior and encourage positive social development. Given its dynamic and intricate characteristics, addressing the propagation of crime requires an approach that considers the broader system dynamics. This paper considers a model with a criminal population, a non-criminal population, and a population convicted of a crime. We study the local and global stability of this model. After that, we consider a switched system where two parameters are switched, i.e., the law enforcement parameter and the fine imposition parameter. The switch here plays a vital role as security deployment is based on the situation and even depends on time/place/weather. Stability is analyzed for this switched system in two sub-parts: arbitrary and periodic switching. At the end, we give a detailed example with numerical simulation to support the stability results.