Study On Optimal Tax Of Three Leslie-Gower Predator-prey Models

This paper consists of three parts:Firstly, the optimal taxation of Leslie-Gower predator-prey model with a prey refuge and modified Leslie-Gower term is considered in this paper. By using of Routh-Hurwitz method, the stability of the equilibrium is discussed. From constructing a suitable Lyapunov function, the unique positive equilibrium point of the model is obtained, which is also globally stable. Moreover, optimal equilibrium solution of the control problem is derived according to Pontryagin Maximum Principle, that is, we obtain the optimal taxation policy of the model.Secondly, the optimal taxation of Leslie-Gower predator-prey model with harvest incorporating a prey refuge is considered in this paper. By Routh-Hurwitz method again, the stability of the equilibrium is discussed. Further, we construct a suitable Lyapunov function and show the fact that the unique positive equilibrium point of the model is globally stable. Moreover, by Pontryagin Maximum Principle, the optimal taxation policy of the model is derived.Finally, the optimal taxation of Leslie-Gower predator-prey model with a prey refuge is considered in this paper. In view of Routh-Hurwitz method, the stability of the model of the equilibrium for the model is discussed. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium point of the model is globally stable. Furthermore, the optimal taxation policy of the model is derived by means of Pontryagin maximum principle.