Simultaneous multiple capture in the presence of evader's defenders

We consider a conflict-controlled process with the participation of three types of controlled objects: a group of pursuers, an evader, a group of defenders of the evader. Dynamic and inertial capabilities of all controlled objects are the same. The evader and the group of defenders act cooperatively. The group of pursuers is the other side of the conflict. If the positions of the pursuer and the defender of the evader coincide then both players die and cease to participate in the conflict-controlled process. In a conflict controlled process multiple capture of an evader occurs when a given number of pursuers catch the evader, and capture moments may not coincide. If (not necessarily least) capture moments coincide then nonstrict simultaneous multiple capture of the evader occurs. Finally, simultaneous multiple capture of the evader occurs when least capture moments appear identical. We obtain necessary and sufficient conditions for simultaneous multiple capture of the evader in terms of initial positions of the participants and other parameters of the conflict-controlled process.