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 points 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. The model with weak Allee effect has at most three positive equilibrium points 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 different bifurcations, such as saddle–node, Hopf and Bogdanov–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 sources for predators.

考虑具有功能响应Holling II型，捕食者具有Allee效应且具有通才捕食者的捕食者－被捕者模型。结果表明，具有强Allee效应的模型在第一象限中最多具有两个正平衡点，一个始终是鞍点，而另一个则表现出多重稳定性现象，因为该平衡点可以是稳定的也可以是不稳定的。Allee效应较弱的模型在第一象限中最多具有三个正平衡点，一个总是鞍点，另外两个可以是稳定或不稳定节点。此外，当参数在系统参数的较小邻域中变化时，模型将经历不同的分叉，例如鞍形节点，Hopf和Bogdanov-Takens叉形。而且，