Forschungsgruppe ORCOS
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Cycles of Violence: A Dynamic Control Model

In a joint work J. Calkins, G. Feichtinger, G. Tragler and V. Veliov proposed and investigated a dynamic control model of the evolution of the level of crime committed by high rate offenders (about 80% of the total crime in USA is such). State components of the model are the number of high rate offenders, and the general level (reputation) of violence. The perception of the latter is important because it could itself be a violence promoter, since it determines the likelihood that a confrontation with a violent individual escalates to lethal violence.

The model consists of two nonlinear ordinary differential equations,
where some of the parameters are chosen as possible control variables (the main one is the rate of exit from the violent population, which can be enhanced by criminal justice sanctions). The objective function consists of the discounted costs for the society of the criminal activities of the high rate offenders, and the control costs.

A complete sensitivity analysis is carried out both at the steady state of the uncontrolled model, and at the optimal steady state of the optimization model, the base parameter values being evaluated from real data. Cyclic optimal behavior has also been obtained, but damped oscillations are typical for realistic parameter values.