具有阈值控制策略的害虫-天敌模型的动力学分析

Dynamics of a Pest-Natural Enemy Model with a Threshold Control Strategy

摘要: 本研究根据 IPM 策略，将所提出的模型以害虫数量作为阁值指标，以此来刻画只有当害虫数量达 到阁值时才对其进行综合害虫治理的策略，通过化学和生物防治相结合，将 Leslie-Gower 模型扩 展为非光滑 Filippov 系统。 为了使害虫种群保持在给定的经济阁值 ET 或以下，利用 Filippov 凸方法和 Filippov 系统相关的定性分析理论，分析了模型在不同阁值的全局动力学，得到实平衡 点和伪平衡点的全局稳定性。 研究表明，在不同阁值范围下，增加自然天敌的释放量以及减少杀 虫剂的用量能有效避免害虫数量爆发，从而为综合害虫治理提供策略和方法。

Abstract: In this study, based on the IPM strategy, the proposed model uses the pest popu- lation as a threshold indicator to depict the strategy of integrated pest management only when the pest population reaches the threshold, and extends the Leslie-Gower model to a non-smooth Filippov system by combining chemical and biological control. In order to keep the pest population at or below a given economic threshold ET, the global dynamics of the model at different thresholds were analyzed by using the Filippov convex method and the qualitative analysis theory related to the Filippov system to obtain the global stability of the inner equilibrium and pseudo-equilibrium points. The study shows that increasing the release of natural enemies and decreasing the amount of insecticides can effectively avoid the outbreak of pest population in different threshold ranges, thus providing strategies and methods for integrated pest management.