Evasion from “soft capture” in a cone in a fourth order game

A problem of conflict interaction of one evader with a group of pursuers is considered. All players have equal dynamic capabilities. The motion of each player is defined by a fourth order differential equation. An evader has full information, and pursuers know positions of all players only. A capture is defined as equality of accelerations, velocities and positions of players. It is assumed that initial position, velocity and acceleration of an evader are inside of the given cone. It is also assumed that a third order derivative, defining evader's path, is initially inside of this cone too. It is proved that if the number of pursuers is less than the space dimension, then runaway occurs.