Methods: The data were drawn from 52 abstinent young adults in sustained recovery from substance abuse (mean age = 22.6, female = 15). Participants provided an average of 23.4 days of daily diary data by end-of-day collections. Latent differential equation models were fit to self-reported daily substance use cravings and negative affect. Particularly, the acceleration of each outcome was predicted by its instantaneous level (i.e., displacement from equilibrium point) and linear slope (i.e., velocity). Coupled model was fit to examine the reciprocal relationship between negative affect and craving as coupled systems.
Results: Both substance use cravings and negative affect could be fit to damped linear oscillator model, with significant oscillating parameters (η = -.94 and -.61, respectively), but no significant damping parameter (ζ = -.02 and .00, respectively). Negative affect demonstrated an oscillating period of 8.1 days, while substance use cravings demonstrated a period of 6.5 days. After controlling for individual average levels of substance cravings and negative affect, social support coping strategy could predict individual difference in the oscillating parameter of substance use craving (B = .34, p = .054).
Discussion: Dynamical systems models provide a unique approach to understand recovery from substance use as a dynamic system. The current results suggest that substance use craving and negative affect, two risk factors of relapse, can be understood as a stable oscillating system without amplifying or damping magnitude in the context of abstinence maintenance. Higher level of support seeking coping strategy is associated with slower individual oscillating frequency (i.e., longer oscillating period), which could be predictive of better long term recovery outcome. Findings from this line of research would enhance our understanding on the mechanism of relapse and identifying targets for continuing monitoring and personalized intervention.