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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.
MSC:
92D40Ecology
34A37Differential equations with impulses
34C25Periodic solutions of ODE
65C20Models (numerical methods)
34D05Asymptotic stability of ODE
34D23Global stability of ODE
Keywords:
persistence