Bifurcation patterns of a discrete prey–predator model subject to slow–fast effect, Allee effect, and complex network

Abstract This study explores a discrete-time predator–prey model characterized by Michaelis–Menten-type predation, incorporating the Allee effect to account for its impact on prey population dynamics. The analysis focuses on equilibrium characterization and bifurcation phenomena near the interior fixed point, with a particular emphasis on their ecological implications. The model exhibits a spectrum of bifurcation phenomena, notably period-doubling and Neimark–Sacker bifurcations, for which the relevant non-degeneracy conditions are analytically verified. To stabilize the system’s complex dynamics, the Ott–Grebogi–Yorke control method is implemented. Beyond isolated interactions, the study extends to a networked structure, revealing how coupling strength and network topology impact population dynamics. Numerical simulations validate the theoretical insights through local dynamical classifications, Lyapunov exponent computations, phase space analysis, and bifurcation diagrams, providing a rigorous exploration of the system’s stability and transition mechanisms.