Staged-structured Lotka–Volterra predator–prey models for pest management

In this paper, 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 Liapunov stability theorem, we obtain the condition for the global asymptotical stability of the trivial equilibrium (i.e., pest-eradication equilibrium). In the second model, impulsive biological control is taken. By use of the Floquet’s theorem, small-amplitude perturbation method and comparison techniques, we get the condition which guarantees the global asymptotical stability of the pest-eradication periodic solution. The sufficient condition for the permanence of the impulsive system is also obtained.