A stage-structured predator-prey model with Crowley-Martin functional response

Abstract

<p style='text-indent:20px;'>A stage-structured predator-prey model with Crowley-Martin functional response is formulated and analyzed to investigate the impaction of predator maturity delay and predator interference on the dynamics of the system. It is shown that the net reproduction number of the system determines its threshold dynamics: the system is permanent if and only if the net reproduction number is larger than one unit, otherwise the predators go extinct; Moreover, given that the system is permanent, the unique coexistence equilibrium is shown to be globally asymptotically stable provided that the predator's interference is large enough; Numerical simulations are also performed to explore the effects of predator maturity delay and predator's interference on the stability of interior equilibrium. It is indicated that an increase of maturity delay of the predator will enlarge its extinction risk and may also enrich dynamics of the system in the sense of bringing stability switches of the coexistence equilibrium; and that an increase of predator's interference may lead to stability switch of coexistence equilibrium from unstable to stable, implying that a large predator's interference can be stabilizing.</p>