Optimal synchronizability of networks

B. Wang, T. Zhou, Z. L. Xiu and B. J. Kim ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2007, vol. 60, issue 1, 89-95

Abstract: We numerically investigate how to enhance synchronizability of coupled identical oscillators in complex networks with research focus on the roles of the high level of clustering for a given heterogeneity in the degree distribution. By using the edge-exchange method with the fixed degree sequence, we first directly maximize synchronizability measured by the eigenratio of the coupling matrix, through the use of the so-called memory tabu search algorithm developed in applied mathematics. The resulting optimal network, which turns out to be weakly disassortative, is observed to exhibit a small modularity. More importantly, it is clearly revealed that the optimally synchronizable network for a given degree sequence shows a very low level of clustering, containing much fewer small-size loops than the original network. We then use the clustering coefficient as an object function to be reduced during the edge exchanges, and find it a very efficient way to enhance synchronizability. We thus conclude that under the condition of a given degree heterogeneity, the clustering plays a very important role in the network synchronization. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Keywords: 89.75.-k Complex systems, 05.45.-a Nonlinear dynamics and chaos, 05.45.Xt Synchronization; coupled oscillators, (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1140/epjb/e2007-00324-y

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