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Bifurcations in a Model of Criminal Organizations and a Corrupt Judiciary
G S Harari1, L H A Monteiro1,2
1Escola de Engenharia, Universidade Presbiteriana Mackenzie, São Paulo 01302-907, SP, Brazil.
Abstract:
Let a population be composed of members of a criminal organization and judges of the judicial system, in which the judges can be co-opted by this organization. In this article, a model written as a set of four nonlinear differential equations is proposed to investigate this population dynamics. The impact of the rate constants related to judges' co-optation and ex-convicts' recidivism on the population composition is explicitly examined. This analysis reveals that the proposed model can experience backward and transcritical bifurcations. Also, if all ex-convicts relapse, organized crime cannot be eradicated even in the absence of corrupt judges. The results analytically derived here are illustrated by numerical simulations and discussed from a crime-control perspective.
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