A low-order discrete dynamical system (DDS) for finite-rate chemistry of H2-air combustion is investigated in 3D. For H2-air reactions, a nine-step mechanism with N2-dilution and a twelve-step mechanism with reacting N2 are studied via the DDS. Both isotropic and anisotropic assumptions are employed when constructing regime maps and studying bifurcation parameter sequences. As input to the DDS, physical quantities from an experimental combusting turbulent flow are used. Numerical solutions consisting of time series of velocities, species mass fractions, temperature, and the sum of mass fractions are analyzed. Numerical results from the DDS are compared with experimental data at a selected location. The comparisons show the DDS can mimic turbulent combustion behaviors in a qualitative sense, and the time-averaged computed results of species concentrations are quantitatively close to those of the experimental data.