Yang Jin, Tan Yuanshun
a College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing , People's Republic of China.
J Biol Dyn. 2018 Dec;12(1):527-550. doi: 10.1080/17513758.2018.1479457.
We establish a Holling II predator-prey system with pesticide dose response non-linear pulses and then study the global dynamics of the model. First, we construct the Poincaré map in the phase set and discuss its main properties. Second, threshold conditions for the existence and stability of boundary periodic solution and order-[Formula: see text] periodic solutions have been provided. The results show that the pesticide dose increases when the period of control increases, while it will decrease as threshold increases. Sensitivity analyses reveal that critical condition for the stability of boundary periodic solution is very sensitive to control parameters and pesticide doses. The bifurcation analysis reveals that the proposed model exists complex dynamics. Compared to the model with fixed moments, it demonstrates that the density of pest population not only can be controlled below the threshold but also can avoid some negative effects due to pesticide application, confirming the importance of biological control.
我们建立了一个具有农药剂量响应非线性脉冲的Holling II捕食者 - 猎物系统，然后研究该模型的全局动力学。首先，我们在相集中构造庞加莱映射并讨论其主要性质。其次，给出了边界周期解和[公式：见原文]阶周期解存在性和稳定性的阈值条件。结果表明，随着控制周期的增加，农药剂量增加，而随着阈值的增加，农药剂量将减少。敏感性分析表明，边界周期解稳定性的临界条件对控制参数和农药剂量非常敏感。分岔分析表明所提出的模型存在复杂动力学。与具有固定时刻的模型相比，它表明害虫种群密度不仅可以控制在阈值以下，而且可以避免由于施用农药带来的一些负面影响，证实了生物控制的重要性。
