Describing and Controlling Multivariate Nonlinear Dynamics: A Boolean Network Approach

We introduce the Boolean network method, a discrete-time dynamical system method, to model the nonlinear dynamics in multivariate systems and to control the system moving to desired state(s). We introduce this method in three steps: (1) inference of the temporal relations between multiple binary variables as Boolean functions, (2) extraction of attractors based on the inferred dynamics and assignment of desirability for each attractor, and (3) design of network control to direct a psychological system toward a desired attractor by identifying how the Boolean network needs to be updated.To demonstrate how the Boolean network can describe and prescribe control for emotion regulation dynamics, we applied this method to data from a study of how children regulate their anger during a frustrating task using bidding and/or distraction (N = 120, T = 480 seconds). Network control strategies were designed to move the child into attractors where anger is OFF. The sample shows heterogeneous emotion regulation dynamics across children in 22 distinct Boolean networks, and heterogeneous control strategies regarding which behavior to perturb and how to perturb it. The Boolean network method provides a novel method to describe nonlinear dynamics in multivariate psychological systems and a control method to guide nonlinear psychological systems toward desired goals.