Attraction Region for the Classical Lotka-Volterra Predator-Prey model Caused by impulsive Effects
Attraction Region for the Classical Lotka-Volterra Predator-Prey model Caused by impulsive Effects
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DOI：
10.1007/s12346-021-00482-w
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发表时间：
2021-07-01
影响因子：
1.4
通讯作者：
Ishihara, Yoshiki
中科院分区：
文献类型：
--
作者：
Sugie, Jitsuro;Ishihara, Yoshiki
不连续现象出现在各个研究领域。脉冲微分方程常用来模拟这种不连续的动力学。研究了具有脉冲效应的Lotka-Volterra捕食者-食饵模型。在建模中，考虑到捕食者和被捕食者的内部平衡与当前种群的比率，加入了脉冲。在这种情况下，脉冲和下一个脉冲之间的时间间隔不受相同的限制。通过对相邻脉冲之间的时间间隔和脉冲效应量的研究，给出了内部平衡点全局渐近稳定的简单充分条件和吸引区估计的充分条件。我们的结果表明，对于Lotka-Volterra捕食者-食饵模型，脉冲控制可以减少捕食者和捕食者种群的变化，使两者能够稳定共存。
Discontinuous phenomena appear in various research fields. Impulsive differential equations are often used to model such discontinuous dynamics. This study deals with the Lotka-Volterra predator-prey model dominated by impulsive effects. In the modeling, impulses are added considering the ratios of the interior equilibrium to the current populations of the prey and predator. In this case, there is no restriction of the time interval between the impulse and the next impulse being the same. By focusing on the time interval between impulses adjacent to one another as well as the impulsive effect amount, a simple sufficient condition for the interior equilibrium to become globally asymptotically stable and sufficient conditions that are useful for estimating an attraction region are provided. Our results reveal that impulse control for the Lotka-Volterra predator-prey model can reduce the variation in the population of the prey and predator and enable the stable coexistence of both.