Run-and-Tumble Escape in Pursuit-Evasion Dynamics of Intelligent Active Particles

The pursuit-evasion game is studied for two adversarial active agents, modelled as a deterministic self-steering pursuer and a stochastic, cognitive evader. The pursuer chases the evader by reorienting its propulsion direction with limited maneuverability, while the evader escapes by executing sharp, unpredictable turns, whose timing and direction the pursuer cannot anticipate. To make the target responsive and agile when the threat level is high, the tumbling frequency is set to increase with decreasing distance from the pursuer; furthermore, the range of preferred tumbling directions is varied. Numerical simulations of such a pursuit-target pair in two spatial dimensions reveal two important scenarios. For dominant pursuers, the evader is compelled to adopt a high-risk strategy that allows the pursuer to approach closely before the evader executes a potentially game-changing backward maneuver to pull away from the pursuer. Otherwise, a strategy where the evader tumbles forward with continuous slight adjustments of the propulsion direction can significantly increase the capture time by preventing the pursuer from aligning with the target propulsion direction, while maintaining the persistence of the target motion. Our results can guide the design of bioinspired robotic systems with efficient evasion capabilities.