  Cluster synchronization is a phenomenon in which oscillators in a given
network are partitioned into synchronous clusters. As recently shown, diverse
cluster synchronization patterns can be found using network symmetry when the
oscillators are identical. For such symmetry-induced cluster synchronization
patterns, subsets called intertwined clusters can exist, in which every cluster
in the same subset should synchronize or desynchronize concurrently. In this
work, to reflect the existence of noise in real systems, we consider networks
composed of nearly identical oscillators. We show that every cluster in the
same intertwined cluster set is nearly synchronized concurrently when the
nearly synchronous state of the set is stable. We also consider an extreme case
where only one cluster of an intertwined cluster set is composed of nearly
identical oscillators while every other cluster in the set is composed of
identical oscillators. In this case, deviation from the synchronous state of
every cluster in the same set increases linearly with the magnitude of
parameter mismatch within the cluster of nearly identical oscillators. We
confirm these results by numerical simulation.
