A new stage structured predator-prey Gomportz model with time delay and impulsive perturbations on the prey

In this paper, we formulate a robust prey-dependent consumption predator-prey Gomportz model with periodic harvesting (catching or poisoning ) for the prey and stage structure for the predator with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and ecological study. By use of the discrete dynamical system determined by the stroboscopic map, we obtain a 'predator-extinction' periodic solution. Further, we show it is globally attractive when some parameters of the system are under appropriate conditions. By using the theory on delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the system. In this paper, the main feature is that we introduce time delay and pulse into the predator-prey (natural enemy-pest) model with stage structure, exhibit a new modeling method which is applied to investigate delay impulsive differential equations, and give some reasonable suggestions for pest management.