<p>This paper investigates the complex dynamics of a discrete-time prey-predator model incorporating both the strong Allee effect and predator-induced fear. We conduct a thorough bifurcation analysis, focusing on codimension-one bifurcations, including Neimark–Sacker, period-doubling, and transcritical bifurcations, as well as codimension-two bifurcations, such as the Bogdanov–Takens bifurcation. Our results indicate that the Allee effect plays a crucial role in shaping system stability and introduces bi-stability, where stable coexistence equilibria and periodic cycles coexist for specific parameter ranges. Additionally, fear effects significantly alter the system’s stability by reducing predator efficiency, effectively delaying the onset of chaos, and stabilizing population dynamics under certain conditions. Through detailed numerical simulations, we establish a clear link between bifurcation structures and observed dynamical transitions, showing how variations in key parameters lead the system through periodic, quasiperiodic, and chaotic behaviors. These findings provide novel insights into the interplay between fear dynamics, the Allee effect, and ecological stability, offering a deeper understanding of how bifurcations govern transitions in population dynamics.</p>