The geometrical structure of the phase space and bifurcations in the c
omplex Lorenz model are investigated. It is shown that the hierarchy o
f bifurcations in a single-mode laser with detuning of the resonator f
requency from the frequency of a spectral line is similar to the hiera
rchy of bifurcations of the logistic map. (C) 1998 American Institute
of Physics. [S1063-7842(98)00108-1].