Dynamic Behaviors of a Stage Structure Commensalism System with Holling type II Commensalistic Benefits

Noting the fact that commensal species that behave as foragers are subject to the constraints of handling time, a two species commensalism model with Holling type II commensalistic benefits and stage structure is proposed and studied. We first show that among four possible equilibria, host-only equilibrium and positive equilibrium are possible asymptotically stable. Next, we establish a powerful lemma on the global stability property of the single species stage structured model with linear perturbation on mature species. By applying this lemma and the differential inequalities theory, sufficient conditions which ensure the global attractivity of the host-only equilibrium and positive equilibrium are obtained, respectively. Our results generalize some known results.