<p>The discrete-time models play a crucial role in illustrating the interplay among concentration changes of different chemical substances in chemistry. This paper investigates the complex dynamics of a discrete-time chemostat model. First, we establish the existence condition of a fixed point and then explore the stability conditions of all fixed points. Using critical normal form theory, codimension-one bifurcations, viz. fold, period-doubling, and Neimark-Sacker bifurcations, are addressed near all fixed points. Further, R4 resonance bifurcation of codimension-two is also explored when two parameters are varied near a positive fixed point. In the discrete-time chemostat model, the codimension-two R4 resonance is observed as oscillations with a highly periodic stable cycle. This implies that both concentrations can undergo periodic oscillations, displaying across various stable cycles. Finally, software experiments are presented to validate the obtained analytical results. The findings of this study are highly innovative and hold significant theoretical value in managing the concentrations of diverse chemical substances.</p>