Uniqueness and global stability of positive stationary solution for a predator-prey system

In this paper, we are concerned about a predator-prey model with Beddington-DeAngelis functional response, in which a protection zone is set for the prey. In a previous paper, it has been shown that the coefficient k measuring the mutual interference between predators in the Beddington-DeAngelis functional response plays a crucial role in the predator-prey system. As k is large enough, there exists a unique globally stable positive stationary solution except a special case. By introducing an equivalent system, this paper reveals that the uniqueness and global stability still holds true in the special case.