The differential game “Cossacks–robbers” on time scales

Abstract

In finite-dimensional Euclidean space, we address the problem of simple pursuit of a group of evaders by a group of pursuers in a given time scale with equal opportunities for all participants. The set of controls of each participant is a sphere of unit radius with its center at the origin. The goal of the group of pursuers is to catch all evaders. The goal sets are the origin. The goal of the evaders is the opposite one, namely, for at least one evader to avoid capture. Conditions for solvability of the local and global problems of evasion and the upper and lower estimates of the minimal number of evaders avoiding a given number of pursuers from any initial positions are obtained.