<p>This study analyzes the dynamics of a discrete-time commensalism system derived via the forward Euler method from a continuous model. It examines the existence and stability of all fixed points in the system. Additionally, at the positive fixed point, it demonstrates that a period-doubling bifurcation occurs in the system. The theoretical results are further supported by numerical simulations showing how changes in the system’s parameters can drive transitions to chaos from stability and even to extinction of species. Our results underscore that discrete-time models possess much more complex dynamics compared to their continuous-time counterparts. Specifically, the discrete-time model not only experiences period-doubling bifurcation but also exhibits chaotic behavior, highlighting the intricate and rich nature of ecological interactions in discrete time. This study emphasizes the importance of using discrete models to fully capture the spectrum of possible dynamics in ecological systems, as they can reveal complex behaviors, such as bifurcation and chaos, that are often not apparent in continuous-time models. These insights have significant implications for understanding ecological dynamics and for the accurate modeling of real-world ecological interactions.</p>