This study focuses on the stationary characteristics of oblique detonation across various reaction rate distributions by using two-dimensional Euler equations coupled with a two-step kinetic model, focusing on the effects of the reduced activation energy and the exothermic reaction rate constant. The results show that increasing the reduced activation energy while decreasing the rate constant of the exothermic reaction postpones the initiation of oblique detonation and stabilizes the initiation structure. This paper innovatively uses these two parameters to regulate the exothermic reaction rate distribution while ensuring that the lengths of the induction and exothermic reaction zones remain constant. It is found that the exothermic reaction rate distribution significantly affects the stationary characteristics of oblique detonation waves. For a constant exothermic zone length, as the activation energy increases, the initiation position of the oblique detonation shifts downstream until it reaches a specific critical threshold. Beyond this point, the initiation structure of the oblique detonation undergoes a rapid transition to instability, evolving into an unstable oblique detonation configuration. This critical behavior occurs because cases with larger activation energy exhibit heightened sensitivity to overdrivenness.