In this study, a 1-step and a 2-step globalized model are used to investigate the competition between chemical kinetics and volumetric expansion. Parametric studies have been conducted to better understand how the critical Damköhler numbers (Da_cr) are related to characteristic chemical time scales: the induction and excitation times. Results show that a gas particle can be cooled down to only 30% of the original temperature and ignite due to strong chemical heat release. For the 1-step model, the contour for Da_cr exhibits bifurcation behaviors for Da_cr > 1. Results for the 2-step model demonstrates a ‘saddle-like’ structure of Da_cr in the q₁-q₂ space (q_i is the reduced activation energy of the i^th chemical step) which disappears as q increases. The Da_cr contours are symmetric about the q₁ = q₂ line. The increase of chemical endothermicity within the induction period leads to an increase of Da_cr.