Delayed pursuit-escape as a model for virtual stick balancing

Abstract

The process of pursuit and escape underlies many biological phenomena ranging from predator–prey interactions, combat and sporting activities. Time delays, τ , arise as a consequence of the time taken to identify the opponent, formulate a strategy, and then act upon it. Here we consider virtual stick balancing (VSB) as a delayed pursuit–escape task. The movements of the target in VSB are programmed to resemble those of balancing a stick at the fingertip. A model of delayed pursuit-escape is developed by assuming that the target movements are governed by a simple random walk and the movements of the pursuer by a delayed random walk biased towards the target when τ = 0. When τ > 0 the movements can become transiently biased away from the target. The model reproduces the oscillatory dynamics and statistical properties of VSB. For both model and VSB, transients occur in which the pursuer moves inappropriately causing increases in tracking error. The presence of a signature, or trigger, for impending escape suggests the possibility that escapes can be predicted before they occur.