Dynamical analysis of a delayed predator-prey system with birth pulse and impulsive harvesting at different moments.

*(English)*Zbl 1229.34123This paper deals with a delayed predator-prey system with birth pulse and impulsive harvesting of the predator population. Firstly, it is proved that all solutions of the system are uniformly ultimately bounded. Then, sufficient conditions for the global attractivity of the prey-extinction periodic solution of the system are given. The permanence of the system is also obtained.

Reviewer: Fatma Karakoc (Ankara)

##### MSC:

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K20 | Stability theory of functional-differential equations |

34K45 | Functional-differential equations with impulses |

92D25 | Population dynamics (general) |

34K12 | Growth, boundedness, comparison of solutions to functional-differential equations |

34K25 | Asymptotic theory of functional-differential equations |

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\textit{J. Jiao} and \textit{L. Chen}, Adv. Difference Equ. 2010, Article ID 954684, 15 p. (2010; Zbl 1229.34123)

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