Stability and bifurcation analysis of a discrete-time predator-prey model with strong Allee effect - Al-Sharawi, Ziyad (2020)
In this paper, we investigate the impact of Allee effect on the stability of a discrete-time predator-prey model with a non-monotonic functional response. The proposed model supports the coexistence of two steady states, and the mathematical features of the model are analyzed based on local stability and bifurcation theory. By considering the Allee parameter as the bifurcation parameter, we provide sufficient conditions for the period-doubling and the Neimark-Sacker bifurcations. Also, sufficient conditions are given to show that increasing the magnitude of the Allee parameter within a certain domain plays a significant role in stabilizing the system.