Abstract: A delayed predator-prey model with stage-structure in prey population and cannibalism in predator population is studied in the present paper.Taking the pregnancy delay of predator population as the bifurcation parameter,local asymptotic stability and existence of local Hopf bifurcation of the model are discussed by using the eigenvalue method,and the critical value of the delay at which the local Hopf bifurcation exhibits is derived.Then,the properties of the Hopf bifurcation are studied by means of the central manifold method.Finally,a simulation example is performed to verify the correctness of the obtained results.

Key words: stage-structure, cannibalism, delay, Hopf bifurcation