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Periodic solution of prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control. (English) Zbl 1263.92053

Summary: A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic systems and the method of successor functions, we obtain a system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solutions are also obtained. Finally, numerical simulations are performed to illustrate our main results.

MSC:

92D40 Ecology
93B52 Feedback control
34A37 Ordinary differential equations with impulses
34C60 Qualitative investigation and simulation of ordinary differential equation models
93C95 Application models in control theory
65C20 Probabilistic models, generic numerical methods in probability and statistics
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