具有非线性收获及食饵避难的Leslie-Gower模型的税收分析
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引用本文:乔运成,李怀玉,黄创霞.具有非线性收获及食饵避难的Leslie-Gower模型的税收分析[J].经济数学,2018,(3):98-104
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作者单位
乔运成,李怀玉,黄创霞 (长沙理工大学 数学与统计学院湖南 长沙 410114) 
中文摘要:研究了具有非线性收获及食饵避难的Leslie-Gower 模型,讨论了该模型解的正性、有界性及正平衡点的存在性. 通过分析特征方程并运用Routh-Hurwitz判别法,得出正平衡点局部渐近稳定的充分性条件. 借助Lyapunov函数以及LaSalle不变原理,研究了正平衡点的全局稳定性. 利用Pontryagin最大值原理,得到了最优税收 τoptimal 以及最优平衡解 (xoptimal, yoptimal, Eoptimal) . 数值模拟与理论结果一致.
中文关键词:财政学  平衡点  稳定性  最优税收
 
Taxation Analysis of Leslie-Gower Model with Nonlinear Harvesting and Prey Refuge
Abstract:Incorporating the nonlinear harvesting and prey refuge, a Leslie-Gower model is investigated. The positivity, boundedness of solutions and the existence of the positive equilibrium are discussed. By analyzing the characteristic equation and using Routh-Hurwitz method, some sufficient conditions for the locally asymptotically stable of the positive equilibrium are derived. With the help of Lyapunov function and LaSalle’s invariance principle, the global stable of the positive equilibrium is studied. Applying Pontryagin maximum principle, the optimal taxation τoptimal and the optimal equilibrium solution (x optimal, yoptimal, Eoptimal) are obtained. Numerical simulations are great well agreement with the theoretical results.
keywords:finance  equilibrium point  stability  optimal taxation
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