A Model of Chaotic Drug Markets and Their Control

Doris A. Behrens, University of Klagenfurt & Vienna University of Technology, Austria

Jonathan P. Caulkins, Carnegie Mellon University & RAND, Pittsburgh, USA

Gustav Feichtinger, Vienna University of Technology, Austria

**Abstract: **This paper explores the idea that drug markets may be
chaotic in a mathematical sense by considering a discrete-time
model of populations of drug users and drug sellers for which
initiation into either population is a function of relative numbers
of both populations. The structure of the system follows that
considered in an arms control context by Behrens, Feichtinger
and Prskawetz (Behrens D.A., Feichtinger G., & Prskawetz A. (1997).
Complex Dynamics and Control of Arms Race. European Journal of
Operations Research, 100, 192-215). The model presented in this
paper summarizes prerequisites for possible chaotic behavior of
the number of addicts and drug dealers frequenting a local drug
market. Interestingly, even if the uncontrolled market dynamics
do not exhibit chaotic patterns, a static intervention like removing
a constant fraction of addicts each time period can easily create
chaos - but even if static control would create chaos, dynamic
controls can be crafted that avoid it. Especially OGY controls
seem to work well for this example.

*Keywords: *drug markets, static and dynamic drug control policies, nonlinear, chaos, OGY control