Global dynamics of a delayed predatorprey model with stage structure and holling type II functional response
The global properties of a delayed predator-prey model with Holling type II functional response and stage structure for both the predator and the prey are investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is discussed. Further, it is proved that the model undergoes a Hopf bifurcation at the coexistence equilibrium. By means of the persistence theory on infinite dimensional systems, it is shown that the model is permanent if the coexistence equilibrium exists. By using Lyapunov functions and the LaSalle invariant principle, it is shown that the trivial equilibrium is globally asymptotically stable when the predator-extinction equilibrium is not feasible, the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main results.
stage structure hopf bifurcation lasalle invariant principle global stability time delay 34k18 34k20 34k60 92d25