Arancibia-Ibarra Claudio, Flores José
School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
Facultad de Ingeniería y Negocios, Universidad de Las Américas, Santiago, Chile.
Math Biosci Eng. 2020 Nov 12;17(6):8052-8073. doi: 10.3934/mbe.2020408.
In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least-weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole population and alternative food source for the weasel population. It is shown that the dynamic is different from the original May-Holling-Tanner predator-prey interaction since new equilibrium points have appeared in the first quadrant. Moreover, the modified model allows the extinction of both species when the Allee effect (strong and weak) on the prey is included, while the inclusion of the alternative food source for the predator shows that the system can support the coexistence of the populations, extinction of the prey and coexistence and oscillation of the populations at the same time. Furthermore, we use numerical simulations to illustrate the impact that changing the predation rate and the predator intrinsic growth rate have on the basin of attraction of the stable equilibrium point or stable limit cycle in the first quadrant. These simulations show the stabilisation of predator and prey populations and/or the oscillation of these two species over time.
在本研究中，我们对传统的May-Holling-Tanner捕食者-猎物模型进行了修改，该模型用于描述伶鼬与田鼠种群之间的相互作用，方法是在田鼠种群上添加一个阿利效应（强和弱），并为伶鼬种群添加替代食物来源。结果表明，由于在第一象限出现了新的平衡点，其动态与原始的May-Holling-Tanner捕食者-猎物相互作用不同。此外，当包含对猎物的阿利效应（强和弱）时，修改后的模型允许两个物种都灭绝，而包含捕食者的替代食物来源表明系统可以支持种群共存、猎物灭绝以及种群同时共存和振荡。此外，我们使用数值模拟来说明改变捕食率和捕食者内在增长率对第一象限中稳定平衡点或稳定极限环的吸引域的影响。这些模拟显示了捕食者和猎物种群的稳定以及/或者这两个物种随时间的振荡。
