Permanence and stability of equilibrium for a two-prey one-predator discrete model

In this letter, a predator-prey system of two-prey one-predator discrete model is investigated. It is proved that the system is permanence under some appropriate conditions. By Jacobian matrix method, a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system. Meanwhile, we give a suitable example for supporting our theoretical result.