•Autoignition and propagation of supersonic ethylene flame is investigated numerically.•The time scale and energy balance methods are developed to study flame stabilization.•The two methods show good validity in the autoignition process of the ethylene flame.•Premixed combustion mode is dominant during the flame autoignition process.•Diffusion combustion mode is dominant when the flame is finally stabilized. Two analysis methods for time scale and energy balance relevant to flame ignition and stabilization in cavity-stabilized flames are developed. The interaction time of hot product in the recirculation zone of the cavity with the surrounding unburned mixture and the reaction induction time of the mixture are estimated in the time scale method. The energy release from chemical reactions and the energy loss due to species exchange in the recirculation zone are included in the energy balance method. The autoignition and propagation of supersonic ethylene flames in a model supersonic combustor with a cavity is investigated first using highly resolved large eddy simulation. The evolutions of the two time scales are then calculated in the ignition process of the supersonic ethylene flames. It is found that the time scale theory is well valid in the flame propagation and stabilization stages. The rates of energy generation and loss are then analyzed in the cavity. It is found that initially the local energy generation rate is relatively small, resulting in slow net energy accumulation in the cavity. Then the energy generation increases due to the intermittent flame propagation in the cavity, whereas the energy loss oscillates consistently since the burned gas leaves the cavity. Also, energy generation and loss are generally balanced in the cavity and all tend to zero after the flame is globally stabilized. The two methods present the characteristic time scales and energy balancing during the transient ignition process for the first time.