论文标题
改良的Leslie-Gower Predator-Prey模型的动力学对猎物和通才捕食者的影响
Dynamics of a modified Leslie-Gower predator-prey model with Allee effect on the prey and a generalist predator
论文作者
论文摘要
考虑了具有功能响应II型功能响应的捕食者 - 捕食模型，猎物中的Allee效应和通才捕食者。结果表明，具有强大效果的模型最多具有两个正平衡点，一个象限始终是鞍点，另一个表现出多稳定性现象，因为平衡点可以稳定或不稳定。虽然第一个象限中最多具有三个正平衡点的模型，但一个始终是鞍点，而其他两个可以是稳定或不稳定的节点。另外，当参数在系统参数的一小邻域中变化时，模型会发生到不同的分叉，例如马鞍节点，Hopf和Bogadonov-Takens分叉。此外，使用数值模拟来说明通过添加Allee效应和捕食者的替代食物来源来说明正平衡点的稳定性。
A predator-prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium point in the first quadrant, one is always a saddle point and the other exhibits multi-stability phenomenon since the equilibrium point can be stable or unstable. While the model with weak Allee effect has at most three positive equilibrium point in the first quadrant, one is always a saddle point and the other two can be stable or unstable node. In addition, when the parameters vary in a small neighbourhood of system parameters the model undergoes to different bifurcations, such as saddle-node, Hopf and Bogadonov-Takens bifurcations. Moreover, numerical simulation is used to illustrate the impact in the stability of positive equilibrium point(s) by adding an Allee effect and an alternative food source for predators.
