Analysis of a diffusive predator-prey system with anti-predator behaviour and maturation delay

The dynamics of a diffusive predator-prey system with anti-predator behaviour and maturation delay subject to Neumann boundary condition is investigated in this paper. The global stability of boundary equilibrium is studied. For coexisting equilibrium, Turing instability induced by diffusion and Hopf bifurcation induced by time delay are studied. By the theory of normal form and center manifold method, the conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived.