  Cluster synchronization in synthetic networks of coupled chaotic oscillators
is investigated. It is found that despite the asymmetric nature of the network
structure, a subset of the oscillators can be synchronized as a cluster while
the other oscillators remain desynchronized. Interestingly, with the increase
of the coupling strength, the cluster is expanding gradually by recruiting the
desynchronized oscillators one by one. This new synchronization phenomenon,
which is named ``scalable synchronization cluster", is explored theoretically
by the method of eigenvector-based analysis, and it is revealed that the
scalability of the cluster is attributed to the unique feature of the
eigenvectors of the network coupling matrix. The transient dynamics of the
cluster in response to random perturbations are also studied, and it is shown
that in restoring to the synchronization state, oscillators inside the cluster
are stabilized in sequence, illustrating again the hierarchy of the
oscillators. The findings shed new light on the collective behaviors of
networked chaotic oscillators, and are helpful for the design of real-world
networks where scalable synchronization clusters are concerned.
