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Global dynamics of a predator-prey system with Holling type II functional response. (English) Zbl 1272.49084
Summary: 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 the feasible equilibria of the system is studied. The existence of an orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and LaSalle’s invariance principle, it is proved that the predator-extinction equilibrium is globally asymptotically stable if the coexistence equilibrium is not feasible, and sufficient conditions are derived for the global stability of the coexistence equilibrium.

MSC:
49N75Pursuit and evasion games in calculus of variations
34H10Chaos control (ODE)
93D20Asymptotic stability of control systems