一类具有时滞和自食现象的捕食者-食饵征税模型(英文)

The Taxation Predator-prey Model with a Time Delay and Cannibalism

研究了一类食饵具有时滞和自食现象的捕食者-食饵征税系统,并在此基础上将税收考虑进去.通过控制税收量来保护资源不被过渡开发,并在适当的假设条件下,讨论了平衡点的存在性.采用RouthHurwitz判别法得到系统正平衡点局部渐近稳定性的条件,以及通过构造Lyapunov函数证明了系统正平衡点是全局渐近稳定的,同时利用Pontrjagin最大值原理给出了最优征税策略,得到了贴现率能够影响捕获种群的利润水平的结论,目的在于既能保护生态系统又能使经济收益达到最大.通过相应的特征方程,分析了时滞对系统的稳定性产生了影响,并得出了当时滞经过τ=τ_O时系统经历Hopf分支的结论.

In this paper,we propose a stage-structured predator-prey model with time delay and cannibalism.In this model,predator resources are protected from being over-exploitation by controlling the amount of taxes.We has discussed the existence of the proposed model's equilibrium,and proved the locally asymptotically stable of system's positive equilibrium by Routh-Hurwitz criterion.The globally asymptoticically stable of the positive equilibrium has also been analysed by constructing a suitable Lyapunov function.We has solved the problem of optimal taxation policy by using Pontryagin's maximum principle,and shown our investigation in this paper that by the corresponding characteristic equations,time delay will cause a stable equilibrium to be unstable,namely,a Hopf bifurcation will take place when time delay passes τ=τ_0.