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Dynamical analysis of a delayed predator-prey system with birth pulse and impulsive harvesting at different moments. (English) Zbl 1229.34123
This 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.

##### 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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