The impact of Allee effect on a predator-prey system with Holling type II functional response
The impact of Allee effect on a predator-prey system with Holling type II functional response
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DOI：
10.1016/j.amc.2010.09.029
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发表时间：
2010-12
期刊：
影响因子：
--
通讯作者：
J. Zu;M. Mimura
中科院分区：
文献类型：
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作者：
J. Zu;M. Mimura
本文将Allee效应引入一类具有Holling Ⅱ型功能反应的捕食者-食饵模型。与不考虑Allee效应的捕食者-食饵模型相比，食饵物种的Allee效应增加了捕食者和食饵的灭绝风险。当捕食者的处理时间相对较短，猎物物种的Allee效应变强时，捕食者和猎物都可能灭绝。此外，还证明了具有Allee效应的模型存在Hopf分支和异宿分支。食饵种群的Allee效应会导致不稳定的周期振荡。当Allee效应的强度或捕食者的处理时间从零开始连续增加时，模型的正平衡点可以从稳定到不稳定，再到稳定，即模型允许稳定性随参数的变化而发生切换.当被捕食者的Allee效应变强时，较长的捕食者处理时间可以稳定共存的稳态。
In this paper, the Allee effect is incorporated into a predator–prey model with Holling type II functional response. Compared with the predator–prey model without Allee effect, we find that the Allee effect of prey species increases the extinction risk of both predators and prey. When the handling time of predators is relatively short and the Allee effect of prey species becomes strong, both predators and prey may become extinct. Moreover, it is shown that the model with Allee effect undergoes the Hopf bifurcation and heteroclinic bifurcation. The Allee effect of prey species can lead to unstable periodical oscillation. It is also found that the positive equilibrium of the model could change from stable to unstable, and then to stable when the strength of Allee effect or the handling time of predators increases continuously from zero, that is, the model admits stability switches as a parameter changes. When the Allee effect of prey species becomes strong, longer handling time of predators may stabilize the coexistent steady state.