One superior pursuer and multiple-evader differential games with two lifelines

This paper investigates a pursuit-evasion game with multiple evaders and a superior pursuer situated on a two-dimensional plane, divided by two lifelines into the play area and goal areas. The goal of the evaders is to reach one of the two goal areas, while the pursuer aims to capture them before they reach the lifeline. This paper constructs barriers without time delay and with time delay, respectively. For each evader, the entire barrier divides the game area into regions of dominance for the evader and pursuer, respectively. Cooperative and non-cooperative strategies between two evaders are studied when the evaders’ positions are within the pursuer's dominance region. We consider the impact of different strategies adopted by the evaders and variations in the distance between the two lifelines on the number of captures by the pursuer. Furthermore, Apollonius circles and Cartesian ovals are used to determine optimal target points for the evaders under different circumstances. Subsequently, we extend the cooperative strategies of the evaders to multiplayer cooperative games, transform them into optimization problems, and use optimization algorithm to derive the cooperative strategies of multiple evaders. Finally, numerical simulations for various cases are presented in this paper.