Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population

This paper studies the dynamic behavior of a discrete-time prey-predator model. It is shown that this model undergoes codimension one and codimension two bifurcations such as transcritical, flip (period-doubling), Neimark-Sacker and strong resonances 1:2, 1:3 and 1:4. The bifurcation analysis is based on the numerical normal form method and the bifurcation scenario around the bifurcation point is determined by their critical normal form coefficients. The advantage of this method is that there is no need to calculate the center manifold and to convert the linear part of the map to a Jordan form. The bifurcation curves of fixed points under variation of one and two parameters are obtained, and the codimensions one and the two bifurcations on the corresponding curves are computed.