  We study two-cluster solutions of an ensemble of generic limit-cycle
oscillators in the vicinity of a Hopf bifurcation, i.e. Stuart-Landau
oscillators, with a nonlinear global coupling. This coupling leads to conserved
mean-field oscillations acting back on the individual oscillators as a forcing.
A reduction to two effective equations makes a linear stability analysis of the
cluster solutions possible. These equations exhibit a $\pi$-rotational
symmetry, leading to a complex bifurcation structure and a wide variety of
solutions. In fact, the principal bifurcation structure resembles that of a 2:1
resonance tongue, while inside the tongue we observe an 1:1 entrainment.
