This paper focuses on introducing a two-dimensional discrete-time chemical model and the existence of its fixed points. Also, the one and two-parameter bifurcations of the model are investigated. Bifurcation analysis is based on numerical normal forms. The flip (period-doubling) and generalized flip bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. To confirm the analytical results, we use the MATLAB package MatContM, which performs based on the numerical continuation method. Finally, bifurcation diagrams are presented to confirm the existence of flip (period-doubling) and generalized flip bifurcations for the glycolytic oscillator model that gives a better representation of the study.