关键词: 食物链模型, Hopf分支, 扩散

Abstract: The Hopf bifurcation of a class of deterministic model, which is three species food chain with diffusion phenomenon and group defense ability subject to Neumann boundary condition, is investigated. By treating the death rate of predator as bifurcation parameter, the stability of the positive constant equilibrium solution is discussed by use of Hurwitz criterion. Then, the conditions which can raise the Hopf bifurcation are given through the theoretical analysis. And also, the normal form method and center manifold theorem are used to study the Hopf bifurcation direction and stability of bifurcating periodic solutions of the spatial nonhomogeneous.

Key words: food chain model, Hopf bifurcation, diffusion