Noise-induced phase transition in the model of human virtual stick balancing

Humans face the task of balancing dynamic systems near an unstable equilibrium repeatedly throughout their lives. The task of inverted pendulum (stick) balancing (Fig. 1a) is an increasingly popular paradigm of studying human control behavior in such situations [1]. In particular, much research has been aimed at understanding the mechanisms of discontinuous, or intermittent control in the context of human balance control [2, 3]. The present paper deals with one of the recent developments in the theory of human intermittent control, namely, the double-well model of noise-driven control activation. The analyzed model of inverted pendulum under control of human operator [4] includes three dynamical variables: stick angle θ, cart velocity υ, and an order parameter ξ describing the cognitive state of the operator in regards to the controlled system. Their dynamics are defined by the equations