一类具有税收措施的浮游植物–浮游动物生态模型的动力学分析

Dynamic Analysis of a Phytoplankton-Zooplankton Ecological Model with Tax Measures

摘要: 本文研究了一类具有税收措施的浮游植物–浮游动物生态模型，探讨了模型平衡点的存在性和局部渐近稳定性，利用Routh-Hurwitz判据得到了平衡点局部渐近稳定的临界条件，依据Pontryagin极大值原理求解出达到最优税收的最优平衡解，得到使社会收入贴现值为最大的税收值。数值模拟工作验证了理论结果的可行性与有效性，并分析了税收措施对模型动力学性态的影响机制。这些研究结果给资源管理者合理制定资源管理政策提供了理论依据。

Abstract: This passage studies a phytoplankton-zooplankton ecological model with tax measure, and dis-cusses the existence and local asymptotic stability of the equilibrium point. According to the Routh-Hurwitz Criterion, the critical conditions for the local asymptotic stability of the equilibrium point are investigated. Using Pontryagin Maximum Principle, the optimal equilibrium solution is obtained to achieve the optimal tax revenue, which can get the tax revenue value to maximize the discount value of social income. Numerical simulation works verify the feasibility and effectiveness of the theoretical results, and analyze the impact mechanism of tax measure on the dynamics of the model. Finally, these results can provide a theoretical basis for resource managers to formulate resource management policies rationally.