Tweaking Synchronisation by Link Addition

Abstract

Natural and man-made networks often possess locally tree-like sub-structures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behaviour. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either a discrete or continuous. Here our main result is that a certain amount of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.

8 pages, 7 figures

References in corpus (6)

• Synchronization in complex networks
• Random graphs with clustering
• Random graphs containing arbitrary distributions of subgraphs
• Performance of networks of artificial neurons: The role of clustering
• Synchronization Properties of Network Motifs
• Random Walks on Complex Networks

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