| Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 8, Iss. 3, Jul, 2004, pp. 375-401 @2004 Society for Chaos Theory in Psychology & Life Sciences A Model of Chaotic Drug Markets and Their Control 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 |