Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 8, Iss. 3, July, 2004, pp. 375-401
@2004 Society for Chaos Theory in Psychology & Life Sciences


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