Pursuit and evasion with temporal non-locality and stochasticity

Abstract

We discuss a new aspect of an old mathematical problem of chase and escape. We consider one group chases another, called “group chase and escape”, by presenting simple models. We have found that even a simple model can exhibit rich and complex behavior. The model has been extended to investigate the effects of (a) stochasticity in chasing and escaping movements, (b) reaction delays (temporal nonlocality) when chasing, and (c) the conversion of caught escapees to new chasers. We show that these effects can add further complexity and result in unexpected behaviors.