Using the comparion theorem of difference equation, persistence theorem of discrete semi-dynamical system and stability of monotonous operator, we gain the boundary, uniform persistence and permanence of the system.

• 应用差分方程的比较原理，离散半动力系统的持久性定理以及单调算子的三分稳定性，获得系统的有界性，一致持久性，永久持久性。