Dynamics of a density-dependent stage-structured predator-prey system with Beddington-DeAngelis functional response

摘要

In this paper, we study the dynamics of a stage-structured predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. First, we derive a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of hyperbolic curves. Then, we provide a sufficient condition to assure the local asymptotic stability of this positive equilibrium by constructing a Lyapunov function. Afterward, by iteratively making use of the comparison theorem, we propose a sufficient condition to assure its global attractiveness. Finally, by investigating types of the ω-limit set instead of making use of the persistence theory, we prove that the predator coexists with the prey permanently if and only if positive equilibria exist.