The Existence Of Stationary Patterns For A Tritrophic Food Chain Model With Diffusion

In this paper, a tritrophic food chain model with difusion and Holling II func-tional response is studied. We mainly discuss the model from the following threeaspects:(1) Stability of nonnegative equilibria and Hopf bifurcation for the corre-sponding ODE system;(2) stability of a positive constant steady state for the PDEsystem with homogeneous Neumann boundary conditions;(3) the existence andnon-existence of non-constant positive steady states for the PDEs. Based on theseresults, we can argue that the efects of difusion rates of three species are diferentin inducing pattern formation. The difusion rates of the prey and top-predator tendto create patterns, while the difusion rate of the middle predator tends to suppresspattern formation.