带有毒素效应功能反应的植物–食植动物模型的脉冲控制研究
Impulsive Control of One Plant-Herbivore Model with Toxin-Determined Functional Response
摘要: 本文考虑了脉冲控制下的一个带有毒素效应功能反应的植物–食植动物模型。理论分析得到了系统关于植物灭绝的平凡周期解的存在性以及它的局部和全局渐近稳定性条件。数值模拟验证了系统存在非常复杂的动力学行为，包括双稳态以及非平凡周期解分支等。结果表明毒素效应不会改变平凡周期解的局部动力学，但它改变了系统的全局稳定性条件。虽然脉冲控制是可行的，但是毒素效应确实增加了控制的难度。
Abstract: In this paper, one impulsive plant-herbivore model with toxin-determined functional response is considered. The trivial periodic solution corresponding to plant extinction, and its local and global asymptotic stability conditions are established. Some dynamical behavior, such as bistability and bifurcation of non-trivial periodic solutions are verified by numerical simulation. The results show the toxin effect does not change the local dynamics of the trivial periodic solutions in the plant- herbivore model with impulsive control, but it changes their global stability conditions. Although impulsive control is feasible in this model, the toxin effect does increase the difficulty of impulsive control.
文章引用：刘天宇, 王帅. 带有毒素效应功能反应的植物–食植动物模型的脉冲控制研究[J]. 应用数学进展, 2021, 10(1): 37-47. https://doi.org/10.12677/AAM.2021.101004

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