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

Abstract

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.