<p>Recent studies have increasingly focused on the stability of predator-prey systems incorporating the Holling functional response and Ricker population model. This work investigates the influence of the Holling effect on a discrete-time predator-prey model, demonstrating through bifurcation theory and the central manifold theorem that the system exhibits period-doubling and Neimark-Sacker bifurcations at equilibrium points. Numerical simulations reveal complex dynamical behaviors, with bifurcation diagrams illustrating transitions from stability to periodic oscillations and chaos. Using phase portraits, Lyapunov exponents, and bifurcation analysis, we show how the Ricker map progresses from order to chaos. Our findings enhance the understanding of predator-prey dynamics and provide insights for ecological population management, highlighting the system’s rich behavior under parameter variations.</p>