Dynamic analysis of a discrete amensalism model with allee effect

This paper concerns with a discretization of a continuous-time amensalism model with Allee effect on the first species. Compared with the continuous analog, the discrete system has different and quite rich dynamical behavior. First, we obtain the existence of fixed points and their local stabili-ties. Then we confirm the occurrence of fold bifurcation and period doubling bifurcation by using the center manifold theorem and bifurcation theory. Fol-lowed is a hybrid control strategy to control the period-doubling bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Nu-merical simulations indicate that Allee effect is beneficial to the stability of the first species to a certain extent. Moreover, when the first species is affected by Allee effect, solutions can quickly approach the corresponding fixed point.