  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.
