一类三种群食物链扩散模型的稳定性

Stability of a Diffusive Model for a Three Species Food Chain

分析了一类由一个食饵种群、一个低级捕食者种群和一个高级捕食者种群组成的三种群食物链扩散模型。利用极值原理和Young不等式得出了解在齐次Neumann边界条件下存在唯一性和一致有界性,并用线性化方法和Lyapunov函数方法讨论了该模型正平衡点的稳定性,分别得到了该模型正平衡点的局部和全局渐近稳定性定理。

In this paper, a three species food chain model consisting of a prey species, a low-level predator speciesand high-level predator species is analyzed. The uniqueness of global existence and uniform boundedness of positive solutions to a three species food chain system with diffusion are proved under homogeneous Neumann boundary condition by peak principle and Young inequality. The stability of positive equilibrium point to the model is discussed, and the local asymptotieal stability and global asymptotical stability are given by linearization method and Lyapunov function respectively.