As the injection total pressure increases, the flow field in the combustion chamber of rotating detonation engine (RDE) becomes complicated and the detonation wave becomes unstable. When the total pressure is high enough, the detonation oscillates periodically and alternates between strong and weak. Under the same injection conditions, no oscillation is observed in two-wave RDE, and the two detonation waves propagate stably in the combustion chamber. The choking ratio of the injection Laval nozzle along the head end is not influenced by the total pressure, the mode of propagation, or the number of detonation waves. And thus the mass flux of RDE can be estimated using the maximum mass flux of the injection Laval nozzle. The specific impulse and thrust of RDE show overall growth as total pressure increases. However, they oscillate with the unstable detonation wave in one-wave RDE at high total pressure.