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Complex dynamics and switching transients in periodically forced Filippov prey-predator system

机译:周期性强迫的Filippov捕食系统中的复杂动力学和切换瞬变

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By employing threshold policy control (TPC) in combination with the definition of integrated pest management (IPM), a Filippov prey-predator model with periodic forcing has been proposed and studied, and the periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. This study aims to address how the periodic forcing and TPC affect the pest control. To do this, the sliding mode dynamics and sliding mode domain have been addressed firstly by using Utkin's equivalent control method, and then the existence and stability of sliding periodic solution are investigated. Furthermore, the complex dynamics including multiple attractors coexistence, period adding sequences and chaotic solutions with respect to bifurcation parameters of forcing amplitude and economic threshold (ET) have been investigated numerically in more detail. Finally the switching transients associated with pest outbreaks and their biological implications have been discussed. Our results indicate that the sliding periodic solution could be globally stable, and consequently the prey or pest population can be controlled such that its density falls below the economic injury level (EIL). Moreover, the switching transients have both advantages and disadvantages concerning pest control, and the magnitude and frequency of switching transients depend on the initial values of both populations, forcing amplitude and ET.
机译:通过采用阈值策略控制(TPC)并结合病虫害综合治理(IPM)的定义,提出并研究了具有周期性强迫的Filippov捕食者模型,假设固有因素的周期性变化会影响周期性强迫猎物的增长率。这项研究旨在解决周期性强迫和TPC如何影响害虫控制。为此,首先利用Utkin的等效控制方法解决了滑模动力学和滑模域问题,然后研究了滑模周期解的存在性和稳定性。此外,已经对包括强迫吸引幅度和经济阈值(ET)的分叉参数的多个吸引子共存,周期增加序列和混沌解的复杂动力学进行了更详细的数值研究。最后,讨论了与害虫暴发有关的转换瞬变及其生物学意义。我们的结果表明,滑动周期解可能是全局稳定的,因此可以控制猎物或害虫的种群,使其密度降至经济损害水平(EIL)以下。此外,开关瞬变在害虫控制方面有优点也有缺点,开关瞬变的大小和频率取决于两个种群的初始值,迫使振幅和ET。

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