The effects of impulsive harvest on a predator–prey system with distributed time delay

A kind of predator–prey system with distributed time delay and impulsive harvest is firstly presented and then the effects of impulsive harvest on the system are discussed by means of chain transform. By using the Floquet’s theory and the comparison theorem of impulsive differential equation, the thresholds between permanence and extinction of each species are obtained as functions of model parameters. It is proved that the impulsive period and the proportion of the impulsive harvest will ultimately affect the fate of each species. Finally, the theoretical results obtained in this paper are confirmed by numerical simulations.