Bifurcation and chaos in a discrete-time predator-prey system with strong Allee effect

A discrete-time system incorporating a strong Allee effect, derived by discretizing the corresponding continuous predator-prey model via the Euler method, is analyzed. Stability analysis reveals that when the predator mortality rate exceeds a critical threshold, two interior equilibria emerge, enabling coexistence of both species. Bifurcation analysis further demonstrates that the system may undergo flip and Neimark-Sacker bifurcations in response to parameter variations. The findings indicate that a strong Allee effect stabilizes the system by generating stable equilibrium points, whereas a weak Allee effect can induce more complex dynamics, such as periodic orbits and chaotic attractors. Additionally, the results highlight the system’s high sensitivity to ecological parameters, including predator population growth rate and environmental protection measures.