异质环境下扩散Holling-Tanner模型正稳态解的全局稳定性
Global Stability of the Positive Steady-State Solution of the Diffusion Holling-Tanner Model in a Heterogeneous Environment
摘要: 考虑异质环境对带有扩散项的Holling-Tanner捕食–食饵模型正稳态解全局稳定性的影响。首先利用抛物方程的比较定理等方法证明了该模型正稳态解的存在性，进一步通过迭代过程，得出了该模型正稳态解的下界。最后通过构造一种新的李雅普诺夫函数，研究Holling-Tanner捕食-食饵模型正稳态解的稳定性：该模型在环境异质下的正稳态解是全局稳定的。
Abstract: Consider the influence of heterogeneous environment on the global stability of the positive steady-state solution of the Holling-Tanner predator-prey model with diffusion term. First, the existence of the positive steady-state solution of the model is proved by the comparison theorem of the parabolic equation, and the lower bound of the positive steady-state solution of the model is obtained through the iterative process. Finally, by constructing a new Lyapunov function, the stability of the positive steady-state solution of the Holling-Tanner predator-prey model is studied: the positive steady-state solution of this model is globally stable under heterogeneous environments.
文章引用：张万红. 异质环境下扩散Holling-Tanner模型正稳态解的全局稳定性[J]. 理论数学, 2021, 11(9): 1665-1672. https://doi.org/10.12677/PM.2021.119185

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