ABSTRACT

This paper intends to simulate a simple artificial society divided into two populations: criminal and non-criminal. The time evolution of the system is modeled using a set of differential equations, borrowing relevant features from the prey-predator, epidemic spread, and harvesting models. Each population can switch type upon interaction. The stability and equilibrium points of this system are examined, concluding that harvesting and interaction rates play an important role in the evolution of the system toward different stable equilibria between populations, which eventually coalesce into one. The results indicate that as long as the harvesting and conversion rates remain sufficiently small, the criminal population thrives. However, when either of the two crosses a certain value, the criminal population becomes extinct.

摘要

本文旨在模拟一个简单的人工社会，分为两个群体：犯罪和非犯罪。系统的时间演化使用一组微分方程建模，借鉴了猎物-捕食者、流行病传播和收获模型的相关特征。每个种群都可以在交互时切换类型。对该系统的稳定性和平衡点进行了检查，得出的结论是收获率和相互作用率在系统向种群之间不同的稳定平衡演变中发挥重要作用，最终合并为一个。结果表明，只要收获和转化率保持足够小，犯罪人口就会蓬勃发展。但是，当两者中的任何一个超过某个值时，犯罪人口就会灭绝。