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Qualitative analysis of the sliding vector field in a Filippov food chain model with integrated pest management strategy

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  • Zhou, Hao
  • Zhang, Qianqian
  • Tang, Sanyi

Abstract

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.

Suggested Citation

  • Zhou, Hao & Zhang, Qianqian & Tang, Sanyi, 2025. "Qualitative analysis of the sliding vector field in a Filippov food chain model with integrated pest management strategy," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    • Handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006490
    DOI: 10.1016/j.amc.2024.129188
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    References listed on IDEAS

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    1. Hossain, Mainul & Kumbhakar, Ruma & Pal, Nikhil, 2022. "Dynamics in the biparametric spaces of a three-species food chain model with vigilance," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. McNeely, Jeff, 2001. "Invasive species: a costly catastrophe for native biodiversity," Land Use and Water Resources Research, University of Newcastle upon Tyne, Centre for Land Use and Water Resources Research, vol. 1, pages 1-10.
    3. Qin, Wenjie & Tan, Xuewen & Tosato, Marco & Liu, Xinzhi, 2019. "Threshold control strategy for a non-smooth Filippov ecosystem with group defense," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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