On Synchronizability of Kleinberg Small World Networks

Abstract

In this paper, the impact of edge-adding probability on both synchronizability and average path length of Klein berg small world networks is investigated. It could be seen from the analysis that two dimensional Klein berg small world networks have similar properties as NW small world networks but Klein berg small world network is more general, that is, the synchronizability becomes stronger as the edge-adding probability increases. Moreover, the average path length of Klein berg small world network decreases with the increasing edge-adding probability. And this phenomenon is verified by numerical simulations on a network of Lorenz oscillators. Then, it could be deduced from the phenomenon observed that compared with the small probabilities of longer distance of the edge-adding, the large probabilities of shorter distance of the edge-adding could achieve better synchronizability. This means the probabilities of the edge-adding play more important than the length of edge-adding to enhance the synchronizability of the small world network.