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<p>The state-dependent impulsive models arising from the biological pest management have been attracted great attention recently, however, most of the proposed models only focus on the very special cases, once the pulse models are nonlinear or nonautonomous, the complete dynamics of the models is far from being solved due to the complexity. Therefore, a Holling II prey-predator model with state-dependent feedback control, rotating pesticide and evolution of resistance in this article is proposed, which makes the model quite different from the existed ones, by employing the Poincaré map for impulsive point series defined in the phase set, and using the comprehensive qualitative analysis of global dynamics in the whole parameter space, the existence, local and global stability of an order-1<i>q</i> periodic solution are obtained. Moreover, the existence of order-2<i>q</i> and order-3<i>q</i> periodic solutions are also been proved theoretically, which indicates that any order periodic solution exists for the proposed model. These findings suggest that rotating pesticide applications can be beneficial for pest control. However, bifurcation analysis also warns managers that blindly increasing control intensity or selecting inappropriate pesticides may shift pest population dynamics from a simple, predictable state to a complex, unpredictable, or even chaotic regime, thereby significantly increasing the difficulty and risk of control failures.</p>

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Integrated pest management via state-dependent impulses and pesticide alternation in predator–prey ecological systems

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Yuanshun Tan,
  • Zhongyi Xiang,
  • Changcheng Xiang,
  • Sanyi Tang,
  • Qianqian Zhang

摘要

The state-dependent impulsive models arising from the biological pest management have been attracted great attention recently, however, most of the proposed models only focus on the very special cases, once the pulse models are nonlinear or nonautonomous, the complete dynamics of the models is far from being solved due to the complexity. Therefore, a Holling II prey-predator model with state-dependent feedback control, rotating pesticide and evolution of resistance in this article is proposed, which makes the model quite different from the existed ones, by employing the Poincaré map for impulsive point series defined in the phase set, and using the comprehensive qualitative analysis of global dynamics in the whole parameter space, the existence, local and global stability of an order-1q periodic solution are obtained. Moreover, the existence of order-2q and order-3q periodic solutions are also been proved theoretically, which indicates that any order periodic solution exists for the proposed model. These findings suggest that rotating pesticide applications can be beneficial for pest control. However, bifurcation analysis also warns managers that blindly increasing control intensity or selecting inappropriate pesticides may shift pest population dynamics from a simple, predictable state to a complex, unpredictable, or even chaotic regime, thereby significantly increasing the difficulty and risk of control failures.