The jet-wedge combinatorial initiation (JWCI) is a novel functional form for initiating an oblique detonation wave (ODW) with reduced total drag within the oblique detonation combustor under the conditions of a low Mach number and low static pressure inflow. It can suppress the instability of the detached ODW. The evolution of the combustion wave during combinatorial initiation is dominated by the intersection between the bow shock wave (BSW) and the oblique shock wave (OSW), and consists of four stages: the shock-induced combustion stage, the shock-deflagration coupling stage, the hybrid combustion stage, and the oblique detonation stage. Three combustion regimes can be formed by using the JWCI: the shock-induced combustion regime, the hybrid combustion regime, and the oblique detonation combustion regime. These regimes have distinct characteristics of combustion and of flow structure that can be controlled by changing two non-dimensional variables: the ratio of momentum flux ( J) and the penetration ratio (PR). This is significant as it can facilitate the application of different combustion regimes under a variety of realistic flight conditions. In this study, the criterion for the transformation of the combustion regime is quantitatively investigated, and show that the structure of the combustion wave does not transform until both non-dimensional variables have reached their respective thresholds. J is crucial for determining the combustion regime and facilitating its transformation but the PR accounts only for the height of the combustion wave structure. The work is beneficial for research on the initiation of the ODW in applications of oblique detonation engines.