In this paper, we introduce the top predator into the Filippov pest-natural enemy system, and propose a three-dimensional Filippov food chain model to address the impact of integrated pest management (IPM) strategies on the sliding dynamics and pest control as well as food chain ecosystems. In particular, the proposed model exists multiple pseudo-equilibria in the sliding region, which result in rich bifurcations in the sliding region including saddle-node, Hopf, sliding-grazing and Bogdanov-Takens bifurcations. These indicate that although the system can stabilize on the sliding region to achieve the purpose of pest control, there are complex dynamics including various sliding bifurcations within the sliding region. Moreover, the main results reveal that the dynamics within the sliding region rely on the IPM strategies, such as top predators within the sliding region tend toward either an interior state or toward extinction under different control measures. This study suggests that the design of control strategies should not only focus on the purpose of control, but also pay attention to the balanced development of the ecosystem.

中文翻译：

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具有综合害虫管理策略的 Filippov 食物链模型中滑动向量场的定性分析


在本文中，我们将顶级捕食者引入 Filippov 害虫-天敌系统，并提出了一个三维 Filippov 食物链模型，以解决综合害虫管理 （IPM） 策略对滑动动力学和害虫防治以及食物链生态系统的影响。特别是，所提出的模型在滑动区域存在多个伪平衡，这导致在滑动区域产生了丰富的分叉，包括鞍节点、Hopf、滑擦和 Bogdanov-Takens 分叉。这些表明，尽管系统可以稳定在滑动区域以达到害虫防治的目的，但存在复杂的动力学，包括滑动区域内的各种滑动分叉。此外，主要结果表明，滑动区内的动力学依赖于 IPM 策略，例如在不同的控制措施下，滑动区内的顶级捕食者倾向于内部状态或灭绝。本研究提示，控制策略的设计不仅应关注控制的目的，还应关注生态系统的均衡发展。