A dynamical systems analysis of adolescent substance abuse

Models from dynamical systems theory were fit to the intraindividual variability in adolescent self-reported cigarette and alcohol use. A dampened linear oscillator model (potentially like a pendulum with friction) and a nonlinear oscillator model with two attractors were compared. The nonlinear oscillator model and two coupled oscillators for cigarette and alcohol use were rejected. Independent dampened linear oscillators for smoking and drinking provided high internal R-2, but were unable to account for a substantial correlation between the acceleration in cigarette usage and alcohol usage; thus evidence was found for an intrinsic self-regulation mechanism in both smoking and drinking behavior, but the hypothesis was rejected that the intrinsic mechanism leading to increases in use in one substance directly predicted increased use in the other substance. Given the hypothesis of in dependent linear oscillators; the sign of the dampening parameter was found to be positive, indicating a system with dynamic instability; a self-regulation mechanism in which small changes in substance use lead to amplified changes after a short period of time.