We present numerical results of the dynamics of a bidirectional single
mode (per direction) line tunable CO2 ring laser with an intracavity
saturable absorber. We employ a rate equation model which includes las
er detuning, Doppler effect of the gain medium caused by gas flowing a
nd the coupling of two counter propagating modes. A lower dynamical th
reshold was found in such a ring laser system comparing with a Fabry-P
erot laser type. In addition to the subcritical Hopf bifurcation and i
nverse cascaded period double bifurcation caused by the competition of
gain and absorber, we found one more inverse period double bifurcatio
n caused by the competition of two counter propagating modes.