标题：Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations
摘要：We propose and study a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations. By using the differential inequality theory we obtain sufficient conditions that ensure the extinction, partial survival, and permanence of the system. By applying the fluctuation lemma we establish sufficient conditions that ensure the extinction of one of the components and the stability of the the other one. For the permanent case, by constructing a suitable Lyapunov function we obtain some sufficient conditions for the globally attractivity of the positive solution of the system. Examples, together with their numeric simulations, show the feasibility of the main results. To ensure the stable coexistence of the two species, the harvesting area should be carefully restricted.
关键词：Commensalism model ; Harvesting ; Partial closure ; Different inequality ; Extinction ; Permanence ; Partial survival ; Lyapunov function ; Fluctuation lemma
