Noisy Pursuit and Pattern Formation of Self-Steering Active Particles

We consider a moving target and an active pursing agent, modeled as an intelligent active Brownian particle capable of sensing the instantaneous target location and adjust its direction of motion accordingly. An analytical and simulation study in two spatial dimensions reveals that pursuit performance depends on the interplay between self-propulsion, active reorientation, and random noise. Noise is found to have two opposing effects: (i) it is necessary to disturb regular, quasi-elliptical trajectories around the target, and (ii) slows down pursuit by increasing the traveled distance of the pursuer. We also propose a strategy to sort active pursuers according to their motility by circular target trajectories.