Dynamics of a Discrete Predator–Prey Model with an Allee Effect in Prey: Stability, Bifurcation Analysis and Chaos Control

In predator–prey interactions, the Allee effect is an important factor in the structuring of ecological communities, the conservation of biodiversity, and the maintenance of ecosystem balance. This study investigates the qualitative behavior of a two-dimensional predator–prey model incorporating the Allee effect on prey for nonoverlapping generations. Since the discrete models display more complex and chaotic dynamics compared with continuous models, the forward Euler method is employed to derive the discrete-time model with Allee effect. The local dynamics of the model near its equilibria are analyzed, and its topological classifications are determined. Furthermore, using bifurcation theory and the center manifold theorem, the existence of instability near the single positive coexistence equilibrium point resulting in flip and Neimark–Sacker bifurcations is demonstrated when intrinsic population dynamics exceed a critical threshold. The occurrence of chaos due to Neimark–Sacker bifurcation is regulated and examined by employing the Ott–Grebogi–Yorke feedback method. Lyapunov exponents are computed to confirm chaotic behavior, and numerical simulations conducted in Matlab and Maple support analytical results.