  Diffusion-induced turbulence in spatially extended oscillatory media near a
supercritical Hopf bifurcation can be controlled by applying global time-delay
autosynchronization. We consider the complex Ginzburg-Landau equation in the
Benjamin-Feir unstable regime and analytically investigate the stability of
uniform oscillations depending on the feedback parameters. We show that a
noninvasive stabilization of uniform oscillations is not possible in this type
of systems. The synchronization diagram in the plane spanned by the feedback
parameters is derived. Numerical simulations confirm the analytical results and
give additional information on the spatiotemporal dynamics of the system close
to complete synchronization.
