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Staged-structured Lotka-Volterra predator-prey models for pest management. (English) Zbl 1152.92029

Summary: Two predator-prey models with stage structure are constructed and investigated. In the first model, continuous biological control is taken. The existence and local stability of two equilibriums are studied. By the Lyapunov stability theorem, we obtain a condition for the global asymptotic stability of the trivial equilibrium (i.e., pest-eradication equilibrium). In the second model, impulsive biological control is taken. By use of Floquet’s theorem, small-amplitude perturbation methods and comparison techniques, we get a condition which guarantees the global asymptotical stability of the pest-eradication periodic solution. A sufficient condition for the permanence of the impulsive system is also obtained.

MSC:

92D40 Ecology
34H05 Control problems involving ordinary differential equations
49N90 Applications of optimal control and differential games
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