To sum up, the following important observations follow from the bifurcation analysis of propane oxidation:(i) For the rate expressions we have used and for the values of RΩRΩ below 1.32 mm, the catalytic reaction dominates, and the first ignition is due to catalytic reaction alone. The lower branch of hysteresis locus is nearly the same as that obtained by considering only the catalytic reaction.(ii) For the kinetics used in this work, thermal coupling between the homogeneous and catalytic oxidation can occur either for higher values of RΩRΩ and/or at short contact times and/or higher inlet mole fractions.(iii) When the catalytic reaction dominates, the solid phase temperature at ignition or MC1568 is always larger than the gas phase temperature. [Since the Lewis number for propane oxidation is greater than unity, the surface/solid temperature after ignition is lower than the adiabatic value, as can be seen in Fig. 11, Fig. 12 and Fig. 13. Further, when residence time is taken as the bifurcation variable, no isolated branches can exist in the adiabatic case. However, this is not the case when the Lewis number is less than unity (especially if it is less than 0.5 as in the case of hydrogen oxidation). Also, the case of fluid temperature being higher than solid temperature can occur when the homogeneous reaction dominates. This case as well as the conditions for possible existence of super-adiabatic temperatures is left for future investigations].(iv) For certain values of parameters (inlet temperatures, residence time and inlet mole fractions), we can obtain a stable intermediate temperature branch where only the catalytic reaction is ignited and the conversion of the reactant is much lower than unity. The rest of the thermally coupled region of hysteresis leads directly to a high conversion, high temperature branch.