  The ubiquitous occurrence of cluster patterns in nature still lacks a
comprehensive understanding. It is known that the dynamics of many such natural
systems is captured by ensembles of Stuart-Landau oscillators. Here, we
investigate clustering dynamics in a mean-coupled ensemble of such limit-cycle
oscillators. In particular we show how clustering occurs in minimal networks,
and elaborate how the observed 2-cluster states crowd when increasing the
number of oscillators. Using persistence, we discuss how this crowding leads to
a continuous transition from balanced cluster states to synchronized solutions
via the intermediate unbalanced 2-cluster states. These cascade-like
transitions emerge from what we call a cluster singularity. At this
codimension-2 point, the bifurcations of all 2-cluster states collapse and the
stable balanced cluster state bifurcates into the synchronized solution
supercritically. We confirm our results using numerical simulations, and
discuss how our conclusions apply to spatially extended systems.
