A delayed diffusive predator-prey system with predator cannibalism

A diffusive predator-prey system with cannibalism and maturation delay in predator subject to Neumann boundary condition is studied in this paper. Instability and Hopf bifurcation induced by time delay are investigated. 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. Some numerical simulations are given to support our results.