  We study the impact of interaction of nodes in a layer of a multiplex network
on the dynamical behavior and cluster synchronization of these nodes in other
layers. We find that nodes interactions in one layer affects the cluster
synchronizability of another layer in many different ways. While multiplexing
with a sparse network enhances the synchronizability multiplexing with a dense
network suppresses the cluster synchronizability with the network architecture
deciding the impact of the enhancement and suppression. Additionally, at weak
couplings the enhancement in the cluster synchronizability due to multiplexing
remains of the driven type, while for strong couplings the multiplexing may
lead to a transition to the self-organized mechanism.
