Kang Baolin, Hou Xiang, Liu Bing
College of Mathematics and Information Science, Anshan Normal University, Anshan 114007, China.
Research Center for Theoretical Ecology, School of Geography and Environment, Jiangxi Normal University, Nanchang 330022, China.
Math Biosci Eng. 2023 May 15;20(7):12076-12092. doi: 10.3934/mbe.2023537.
In this paper, we establish an integrated pest management Filippov model with group defense of pests and a constant rate release of natural enemies. First, the dynamics of the subsystems in the Filippov system are analyzed. Second, the dynamics of the sliding mode system and the types of equilibria of the Filippov system are discussed. Then the complex dynamics of the Filippov system are investigated by using numerical analysis when there is a globally asymptotically stable limit cycle and a globally asymptotically stable equilibrium in two subsystems, respectively. Furthermore, we analyze the existence region of a sliding mode and pseudo equilibrium, as well as the complex dynamics of the Filippov system, such as boundary equilibrium bifurcation, the grazing bifurcation, the buckling bifurcation and the crossing bifurcation. These complex sliding bifurcations reveal that the selection of key parameters can control the population density no more than the economic threshold, so as to prevent the outbreak of pests.
在本文中，我们建立了一个具有害虫群体防御和天敌恒定释放率的综合害虫管理 Filippov 模型。首先，分析了 Filippov 系统中子系统的动力学。其次，讨论了滑模系统的动力学以及 Filippov 系统的平衡点类型。然后，当两个子系统分别存在全局渐近稳定极限环和全局渐近稳定平衡点时，通过数值分析研究了 Filippov 系统的复杂动力学。此外，我们分析了滑模和伪平衡点的存在区域，以及 Filippov 系统的复杂动力学，如边界平衡点分岔、擦边分岔、屈曲分岔和穿越分岔。这些复杂的滑模分岔表明，关键参数的选择可以将害虫种群密度控制在不超过经济阈值的范围内，从而防止害虫爆发。
