The catalytic ignition of H-2/air mixtures over platinum is modeled using a stagnation-point flow model with detailed gas-phase, surface kinetics and transport using an are-length continuation technique. Self-inhibition of the catalytic ignition of H-2/air mixtures is observed in agreement with experiments. For compositions between similar to 0.3 and similar to 15% H-2 in air at atmospheric pressure, hysteresis is created by site competition, while for mixtures with more than similar to 15% H-2 in air, thermal feedback is a prerequisite. It is found that the system shifts from a kinetics-limited regime on the extinguished branch to a transport-limited regime on the ignited branch. However, near ignition, the system tends toward a transport- and kinetics-limited regime. Sensitivity analysis on the reaction preexponentials shows that the competitive dissociative adsorption of H-2 and O-2 and the desorption of H* most affect the catalytic ignition temperature. Reaction path analysis reveals a change in dominant surface reaction paths as a function of feed composition. The effects of strain rate, pressure, and preheating on catalytic ignition are also discussed.