Spontaneously generated ionization wave patterns, which exhibit hyteresis, have been observed to exist in some narrow range of experimental conditions [J. B. Du, C. H. Chiang, and Lin I, Phys. Rev. E 54, 1829 (1996)]. The present work reports a theoretical model for explaining these observations. Including the plasma ionization, losses, and collisions, the phenomenon can be interpreted as a reaction-diffusion problem. It has been found that there exists an internally generated order parameter, which plays an important role in governing the observed hysteresis.
