Describing and Controlling Multivariate Nonlinear Dynamics: A Boolean Network Approach

Abstract

We introduce a discrete-time dynamical system method, the Boolean network method, that may be useful for modeling, studying, and controlling nonlinear dynamics in multivariate systems, particularly when binary time-series are available. We introduce the method in three steps: inference of the temporal relations as Boolean functions, extraction of attractors and assignment of desirability based on domain knowledge, and design of network control to direct a psychological system toward a desired attractor. 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 use bidding to an adult and/or distraction to regulate their anger during a frustrating task (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 is a method with potential to eventually inform the design of interventions that can guide those systems toward desired goals.

Keywords:

• Boolean network
• network control
• psychological systems
• nonlinear dynamics