中文摘要：

在运用微分方程理论研究具有3个年龄阶段的自食单种群模型的基础上将税收考虑进去，分析了一类具有阶段结构的自食单种群征税模型，讨论了平衡点的存在性．在适当的假设条件下，采用Routh-Hurwitz判别法证明了系统正平衡点是局部渐近稳定的，并通过构造Lyapunov函数得到了系统正平衡点的稳定吸引域．同时利用Pontryagin最大值原理给出了最优征税策略，得出了贴现率能够影响捕获种群的利润水平．目的在于既保护生态系统又能使经济收益最大，为生物资源的开发和利用提供可靠的理论依据．

英文摘要：

In this paper, a three life stages structure population model based on cannibalism and taxation is studied by using the theory of differential equation. The existence of equilibrium of the system is discussed. Under appropriate assumption, locally asymptotic stability of the system＇s positive equilibrium is proved by applying Routh-Hurwitz criterion, and the positive equilibrium of the feasible space is obtained by constructing a Lyapunov function. Using Pontryagin~ s maximal principle, the problem of optimal taxation policy is then solved, and it is pointed that the discount rate can affect the economic rent. The objective is to maximize the monetary social benefit as well as conservation of the ecosystem for the development and utilization of biological resources to provide a reliable theoretical basis.