Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model

The discrete Leslie-Gower predator-prey model is studied. The model allows for afluctuating environment. Sufficient conditions which guarantee the permanence of the model are obtained at first, assuming that the coefficients in the model are periodic, the existence of periodic solution are also obtained. Finally, by linearization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution.