  We present the stability analysis of the dark states in the adiabatic passage
for the linear and non-linear lambda and tripod systems in the presence of
amplitude damping (losses). We perform an analytic evaluation of the real parts
of eigenvalues of the corresponding Jacobians, the non-zero eigenvalues of
which are found from the quadratic characteristic equations, as well as by the
corresponding numerical simulations. For non-linear systems, we evaluate the
Jacobians at the dark states. Similarly to the linear systems, here we also
find the non-zero eigenvalues from the characteristic quadratic equations. We
reveal a common property of all the considered systems showing that the
evolution of the real parts of eigenvalues can be split into three stages. In
each of them the evolution of the stimulated Raman adiabatic passage (STIRAP)
is characterized by different effective dimension. This results in a possible
adiabatic reduction of one or two degrees of freedom.
