<p>Pest and disease outbreaks pose significant challenges to agricultural development. This study employs an integrated pest management strategy to mitigate their impact on crops. If pest populations remain below economic thresholds, no intervention is necessary. However, if they exceed these thresholds, control measures are implemented. This paper analyses equilibria stability and the occurrence of Hopf bifurcations. It has been determined that the system exhibits periodic oscillations under specific conditions, triggered by Hopf bifurcations. The sliding mode equations are derived using the Filippov convex method. Numerical simulations indicate complex convergence at various economic thresholds. Additionally, the paper discusses the dynamical characteristics of switching under time delays, specifically, noting that varying time delays cause the system to switch from boundary node to boundary focus bifurcation and from buckling bifurcation to crossing bifurcation. The conclusions offer a reference for designing a Filippov control strategy to enhance crop yield.</p>

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Switching dynamics of a non-smooth Filippov pest control model with time delay and predator cannibalism

  • Zhengwei Ye,
  • Shengwen Deng,
  • Xiangling Liang

摘要

Pest and disease outbreaks pose significant challenges to agricultural development. This study employs an integrated pest management strategy to mitigate their impact on crops. If pest populations remain below economic thresholds, no intervention is necessary. However, if they exceed these thresholds, control measures are implemented. This paper analyses equilibria stability and the occurrence of Hopf bifurcations. It has been determined that the system exhibits periodic oscillations under specific conditions, triggered by Hopf bifurcations. The sliding mode equations are derived using the Filippov convex method. Numerical simulations indicate complex convergence at various economic thresholds. Additionally, the paper discusses the dynamical characteristics of switching under time delays, specifically, noting that varying time delays cause the system to switch from boundary node to boundary focus bifurcation and from buckling bifurcation to crossing bifurcation. The conclusions offer a reference for designing a Filippov control strategy to enhance crop yield.