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Stability Analysis of a Delayed Paranthrene tabaniformis (Rott.) Control Model for Poplar Forests in China

Author

Listed:
  • Meiyan Wang

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Leilei Han

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Yuting Ding

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

Abstract

Forest pests and diseases can diminish forest biodiversity, damage forest ecosystem functions, and have an impact on water conservation. Therefore, it is necessary to analyze the interaction mechanism between plants and pests. In this paper, the prevention and control of a specific pest—namely the larva of Paranthrene tabaniformis (Rott.) (hereinafter referred to as larva)—are studied. Based on the invasion mechanism of the larva in poplar, we establish a delayed differential equation and analyze the existence and stability of equilibria. Next, we assess the existence of a Hopf bifurcation to determine the range of parameters that ensures that the equilibria are stable. Then, we select a set of parameters to verify the results of the stability analysis. Finally, we provide biological explanations and effective theoretical control methods for poplar pests and diseases.

Suggested Citation

  • Meiyan Wang & Leilei Han & Yuting Ding, 2024. "Stability Analysis of a Delayed Paranthrene tabaniformis (Rott.) Control Model for Poplar Forests in China," Mathematics, MDPI, vol. 12(6), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:827-:d:1355333
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    References listed on IDEAS

    as
    1. Lee, Sang Dong & Park, Sohyun & Park, Young-Seuk & Chung, Yeong-Jin & Lee, Buom-Young & Chon, Tae-Soo, 2007. "Range expansion of forest pest populations by using the lattice model," Ecological Modelling, Elsevier, vol. 203(1), pages 157-166.
    2. McTaggart, Ewan & Megiddo, Itamar & Kleczkowski, Adam, 2023. "The effect of pests and pathogens on forest harvesting regimes: A bioeconomic model," Ecological Economics, Elsevier, vol. 209(C).
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