A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response: I, long time behavior and stability of equilibria

We study a ratio-dependent reaction–diffusion system incorporating one prey and two competing predator species under homogeneous Neumann boundary conditions. In this paper, we examine the global attractor and persistence of the system, which characterize the long time behavior of the time-dependent solution, and the stability of all non-negative equilibria of the system. We classify the relations between two competing predators into four categories via domination of one predator over another and weak/strong competition states. These competition states will be the criteria which influence the outcomes of the system. The results include total extinction, competitive exclusion, behavior of a predator driving the extinction of another predator and its prey, behavior of a predator saving its competing predator and prey on the verge of extinction.