Synchronization-based scalability of rings and chains of dense lumps

This paper aims to investigate the scalability of synchronizability for the complex clustering networks of dense rings or chains with the network scale increasing. Our results reveal that the synchronizability of the above complex clustering networks decreases with the network scale increasing for any clustering structures. When the network size is increasing, the increase of the number of clusters decreases the synchronizability much faster than the increase of the size of individual cluster. Moreover, it is found that the ring or the chain structure has much greater influence on weakening the network synchronizability than that of the clustering property.