  In a network of nonlocally coupled Stuart-Landau oscillators with
symmetry-breaking coupling, we study numerically, and explain analytically, a
family of inhomogeneous steady states (oscillation death). They exhibit
multi-cluster patterns, depending on the cluster distribution prescribed by the
initial conditions. Besides stable oscillation death, we also find a regime of
long transients asymptotically approaching synchronized oscillations. To
explain these phenomena analytically in dependence on the coupling range and
the coupling strength, we first use a mean-field approximation which works well
for large coupling ranges but fails for coupling ranges which are small
compared to the cluster size. Going beyond standard mean-field theory, we
predict the boundaries of the different stability regimes as well as the
transient times analytically in excellent agreement with numerical results.
