Stability Analysis Of Two Classes Of Predator-Prey Model With Three Species

In this paper, the stability of two classes of predator-prey model with three species are studied. Firstly, the research problem of the whole paper and its related background are introduced. Secondly, the stability of an Armstrong-McGehee model with two consumers and one biotic resource is discussed. Finally, the stability of a pest epidemic model with infected prey is investigated. Through the stability analysis of two classes of different model, the effect of cross-diffusion coeffcient on the stability of nonnegative equilibrium points for the corresponding model is summarized. The results show that cross-diffusion can induce Turing instability when the cross-diffusion coeffcient take suitable values.