Dynamics of a predator–prey fishery model with birth pulse, impulsive releasing and harvesting on prey

This paper presents a predator–prey fishery model with impulsive effects, which considers transient/nontransient pulse birth and introduces the harvesting and releasing of the prey fish population at different fixed moments of time. We prove that all solutions of the investigated system are uniformly ultimately bounded. Further, the sufficient conditions for the globally asymptotical stability of the predator–extinction boundary periodic solution and the permanence of the system have been subsequently obtained. Finally, the implications of the investigated model for practical fisheries management are illustrated by numerical simulations. It is shown that releasing and harvesting the prey fish population reasonably allow the fish to persist, and thus ensure sustainable development of the fishery resources.