Permanence and Periodic Solution of a Non-autonomous Stage-structure Prey-Predator Model with Cannibalism

A non-autonomous stage-structure prey-predator model with cannibalism for prey is proposed and investigated in this paper. Using the differential inequality theory, sufficient conditions that ensure the system’s permanence are obtained in the general non-autonomous case. For periodic case, by using Brower’s fixed point theorem and constructing a suitable Lyapunov function, sufficient conditions which ensure the existence of unique globally asymptotically stable periodic solutions are obtained. Numeric simulations are carried out to show the feasilibility of the main results.