A food chain system with Holling IV functional responses and impulsive effect. (English) Zbl 1155.92043

Summary: According to biological and chemical control strategies for pest control, our main purpose is to construct a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive effect concerning integrated pest management, and to investigate the dynamic behaviors of this system. By using the Floquet theory and the comparison theorem of impulsive differential equations and analytic methods, we prove that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, a condition for permanence of the system is established. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level.


92D40 Ecology
34A37 Ordinary differential equations with impulses
34C25 Periodic solutions to ordinary differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
34D05 Asymptotic properties of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations


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