This work deals with the consequences on structural stability of Gause type predator-prey
models, when are considered three standard functional responses and the prey growth rate
is subject to an Allee effect.
An important consequence of this ecological phenomenon is the existence of a separatrix
curve dividing the behavior of trajectories in the phase plane. The origin is an attractor
for any set of parameters and the existence of heteroclinic curves can be also shown.
Conditions on the parameter values are established to ensure the existence of a unique
positive equilibrium, which can be either an attractor or a repellor surrounded by one or
more limit cycles.
The influence of the Allee effect on the number of limit cycles is analyzed and the
results are compared with analogous models without this phenomenon, and which main
features have been given in various above works. Ecological interpretations of these
results are also given.