threshold harvesting policy and delayed ratio-dependent functional response predator-prey model

this paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. we study the equilibria of the system before and after the threshold. we show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. the global analysis of the model as well as boundedness and permanence properties are examined too. then we analyze the effect of time delay on the stabilization of the equilibria, i.e., we study whether time delay could change the stability of a co-existence point from an unstable mood to a stable one. the systemundergoes a hopf bifurcation when it passes a critical time delay. finally, some numerical simulations are performed tosupport our analytic results.