Permanence and global attractivity of a discrete pollination mutualism in plant-pollinator system with feedback controls

In this paper, we propose a discrete pollination mutualism in a plant-pollinator system with the Beddington-DeAngelis functional response and feedback controls. By applying the comparison theorem of a difference equation and constructing some suitable Lyapunov functions, sufficient conditions are obtained for the permanence and the extinction of the system. Moreover, under some suitable conditions, we show that the solution of the system is globally attractive. The paper ends by some numerical simulations and a brief discussion.