A delayed Lotka–Volterra model with birth pulse and impulsive effect at different moment on the prey

In this paper, we consider a Lotka–Volterra model with birth pulse and impulsive catching or poisoning for the prey at different moment and stage structure on the predator. We prove that all solutions of the system are uniformly ultimately bounded. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that impulsive effects on the prey play an important role for the permanence of the system. In this paper, the main feature is to introduce birth pulse and impulse catching into Lotka–Volterra model and to give pest management strategies.