机构地区: 东北师范大学数学与统计学院
出 处: 《东北师大学报(自然科学版)》 2014年第2期1-8,共8页
摘 要: 研究了齐次Neumann边界条件下反应扩散对一类食饵具有避难所的LeslieGower模型的影响.利用Routh-Hurwitz判别法判断平衡点的局部稳定性,通过构造合适的Lyapunov函数得到了正平衡点全局渐进稳定的充分性条件,根据Pontryagin最大值原理得到了模型的最优税收策略. In this paper, we study the stability and optimal tax of Leslie-Gower predator-prey model with a prey refuge and diffusion under the homogeneous Neumann boundary condition. We use the Routh-Hurwitz criterion to prove the local stability of the equilibrium points for the model and by constructing Lyapunov function, sufficient conditions of the globally asymptotic stability of the positive equilibrium for the model are obtained. Finally, the optimal taxation policy of the model is studied by using Pontryagin maximum principle.