Global Dynamics of a Predator-Prey Model with Stage Structure and Delayed Predator Response

Abstract EN

A Holling type II predator-prey model with time delay and stage structure for the predator is investigated.

By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed.

The existence of Hopf bifurcations at the coexistence equilibrium is established.

By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists.

By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and the sufficient conditions are obtained for the global stability of the coexistence equilibrium.