Hi zulkarnain,
I agree with asif. If the laser can be pumped strong enough, i.e. r can be made large enough so that the stimulated lifetime becomes as short as the cavity decay time, relaxation oscillations vanish. The physical reason for relaxation oscillations and later instabilities is, that the gain reacts to slow on the light field, i.e. the stimulated lifetime is long in comparison with the cavity decay time.
Regards