Pursuit, herding and evasion: A three-agent model of caribou predation

Motivated by problems of pursuit and evasion in coordinated multi-agent systems, we present a model of pursuit, herding and evasion for three agents: a single pursuer, e.g. a bear, chooses a target point along the line connecting two evaders, and the two evaders, e.g. a mother caribou and her calf, each choose a strategy that trades off evasion and herding. The model is based on feedback control of constant speed steered particles on the plane. Dynamics over a reduced set of shape variables are defined. Parallel-motion shape equilibria are studied, with stability analysis and analytic solutions provided for special cases in the parameter space. Simulation results are also presented that suggest existence of optimal strategies for the bear and the caribou in a game theoretic sense.