A stage-structured predator-prey model with Beddington-DeAngelis functional response

In this paper, a stage-structured predator-prey model with Beddington-DeAngelis functional response is proposed and analyzed. It is assumed in the model that the individuals in each specie may belong to one of two classes: the immature and the mature, the age of maturity is represented by a time delay. By using the persistence theory for infinite dimensional systems, necessary and sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, a set of easily verifiable sufficient conditions is also obtained for the local asymptotic stability and the global attractiveness of the positive equilibrium of the model.