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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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\textit{C. Wei} and \textit{L. Chen}, J. Appl. Math. 2012, Article ID 607105, 17 p. (2012; Zbl 1263.92053)

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### References:

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