A stage-structured predator-prey model of Beddington-Deangelis type

We formulate and study a robust stage structured predator-prey model of Beddington DeAngelis-type functional response. The time delay is the time taken from birth to maturity. The Beddington-DeAngelis functional response is similar to the Holling type 2 functional response but contains an extra term describing mutual interference by predators. First we show that the predator coexists with prey permanently if and only if the predator's recruitment rate at the peak of prey abundance is larger than its death rate. Second, we show that if the system is permanent, then a sufficiently large degree of the predator interference can not only stabilize the system but also guarantee the stability of the system against the increase of the carrying capacity of prey and the increase of birth rate of the adult predator. Third, we show both analytically and numerically that stability switches of interior equilibrium may occur as maturation time delay increases: stability may change from stable to unstable to finally stable, implying that a large delay can be stabilizing.