  The self-starting dynamics of a model for passively mode-locked lasers with
saturable absorber, in which the optical amplifier has a saturable
nonlinearity, is examined. The basic assumption is that the laser will operate
in the mode-locked regime when the continuous-wave regime becomes unstable.
Within the framework of the modulational-instability analysis, a global map for
the laser self-starting criteria is constructed. According to this map, the
saturable nonlinearity enhances the input-field intensity required for laser
self-starting. Analytical expression of the zero modulation-frequency regime of
this threshold input field is derived, which turns out to be valid in the
normal as well as in the anomalous dispersion regime, where evidence of
self-starting is also given.
