A model of chaotic drug markets and their control

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.