Huang Kunlun, Jia Xintian, Li Cuiping
LMIB-School of Mathematical Sciences, Beihang University, Beijing 100083, China.
Math Biosci Eng. 2023 Jul 26;20(8):15524-15543. doi: 10.3934/mbe.2023693.
In this paper, we study a predator-prey system, the modified Holling-Tanner model with strong Allee effect. The existence and stability of the non-negative equilibria are discussed first. Several kinds of bifurcation phenomena, which the model may undergo, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation, are studied second. Bifurcation diagram for Bogdanov-Takens bifurcation of codimension 2 is given. Then, possible dynamical behaviors of this model are illustrated by numerical simulations. This paper appears to be the first study of the modified Holling-Tanner model that includes the influence of a strong Allee effect.
在本文中，我们研究了一个捕食者 - 猎物系统，即具有强阿利效应的修正霍林 - 坦纳模型。首先讨论了非负平衡点的存在性和稳定性。其次研究了该模型可能经历的几种分岔现象，如鞍结分岔、霍普夫分岔和博格达诺夫 - 塔克分岔。给出了二维余维博格达诺夫 - 塔克分岔的分岔图。然后，通过数值模拟说明了该模型可能的动力学行为。本文似乎是首次对包含强阿利效应影响的修正霍林 - 坦纳模型进行研究。
