Dynamics of pursuit and evasion in a heterogeneous herd

We propose and analyze a dynamic model of pursuit and evasion on the plane with a single pursuer and a heterogeneous group of evaders. Heterogeneity in the group of evaders is expressed as heterogeneity in the individual maximum speeds. The goal of the pursuer is to capture a single evader in minimum time. The goal of each individual evader is to avoid capture or else to delay capture for as long as possible. Two cases of sensing among agents are considered: global (all-to-all) sensing, and local (radius-limited) sensing. We present pursuer strategies for optimal target selection that achieve bounded capture time. We propose evasion strategies and prove conditions under which they guarantee capture avoidance. In the case of local sensing, our strategy of evader risk reduction leads to aggregation of the evaders where the slowest evader in a group is the only member with a risk of capture. Our results provide insight into the dynamics of aggregation.