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We theoretically investigate the Doppler effect on optical bistability in an N-type active Raman gain atomic system inside an optical ring cavity. It is shown that the Doppler effect can greatly enhance the dispersion and thus create the bistable behaviour or greatly increase the bistable region, which has been known as the positive Doppler effect on optical bistability. In addition, we find that a positive Doppler effect can change optical bistability from the hybrid dispersion-gain type to a dispersive type. [ABSTRACT FROM AUTHOR]