Abstract. This paper is concerned with the positive steady states of adiffusive Holling type II predator-prey system, in which two predatorsand one prey are involved. Under homogeneous Neumann boundary con-ditions, the local and global asymptotic stability of the spatially homoge-neous positive steady state are discussed. Moreover, the large diffusion ofpredator is considered by proving the nonexistence of non-constant posi-tive steady states, which gives some descriptions of the effect of diffusionon the pattern formation. 1. IntroductionDue to the universal existence of energy transformation, predator-prey sys-tem is very important in describing the population evolution, and it is oneof the dominant themes in both ecology and mathematical ecology. Becauseof the differences in capturing food and consuming energy, a major trend intheoretical work on predator-prey dynamics has been launched so as to derivemore realistic models and functional responses, for example, Lotka-Volterratype [22, 31], Holling type [14], Beddington-DeAngelis type [3, 5] and so on.These models often involve only one predator species and one prey species. Inreality, it is very common that one species is captured by several species in foodchains. In particular, Hixon and Jones [13] found that the density-dependentmortality in demersal marine fishes is often caused by interaction of predationand competition. In a very recent paper, to study how the nonlinear mortalityrate determines the dynamics of such competition models, Ruan et al. [29]proposed the following two predators and one prey model with Holling II type
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