Global dynamics of a predator-prey system with Holling type II functional response - Tian, Xiaohong; Xu, Rui (Nonlinear Analysis: Modelling and Control, 2011)
In this paper, a predator-prey system with Holling type II functional response and stage structure is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is studied. The existence of the orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and the LaSalle invariance principle, it is proven that 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.
Keywords: Holling type II functional response; stage structure; periodic solution; LaSalle invariance principle; global stability