Bulletin of the
Korean Mathematical Society BKMS

This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the nonexistence of non-constant positive steady states, which gives some descriptions of the effect of diffusion on the pattern formation.

Keywords: predator-prey system, positive steady state, large diffusion, Holling II type functional response, local/global asymptotic stability

MSC numbers: 35J60, 37B25, 92D25