具有状态反馈脉冲控制的叶螨–捕植螨系统的动力分析
The Dynamic Analysis of the Spider Mite-Phytoseiid Mite System with State-Feedback Impulse Control
摘要: 叶螨取食重要农业植物的叶和果实，是田间农作物的一大害虫，人们利用捕植螨对其进行控制。本文建立了Smith增长且具有Beddington-DeAngelis型功能反应的叶螨–捕植螨系统，并对该系统的有界性，极限环不存在以及平衡点的类型和其稳定性进行了分析。同时，基于这个模型又建立了具有脉冲控制的状态反馈脉冲模型，证明了其阶一周期解的存在性。
Abstract: The spider mites feed on leaves and fruits of important agricultural plants and are a major pest to crops in the field. People use phytoseiidae mites to control them. In this paper, a Smith increased spider mite-phytoseiidae mites system with Beddington-Deangelis functional response is established. The boundedness, the existence of the limit cycle, the types of equilibrium points and their stability of the system are analyzed. At the same time, based on the model, a state feedback impulse model is established to prove the existence of its order-1 periodic solution.
文章引用：杨韶宇, 张蒙. 具有状态反馈脉冲控制的叶螨–捕植螨系统的动力分析[J]. 应用数学进展, 2024, 13(6): 2605-2613. https://doi.org/10.12677/aam.2024.136249

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