Global asymptotical stability of a n+1n+1 dimensional Leslie–Gower predator–prey model

By constructing suitable Lyapunov function, we obtain the global asymptotical stability of n+1n+1 dimensional Leslie–Gower predator–prey models. It is shown that the prey refuge and the proportional harvesting have no influence on the global asymptotical stability of the system, but they can change the position of the unique interior equilibrium. Finally, mathematic analysis shows that if we choose and control the harvesting efforts e,ei appropriately, we can not only harvest the biological resources and achieve the economic interest, but also protect the biological resources.