Polarized networks, diameter, and synchronizability of networks

Details Polarized networks, diameter, and synchronizability of networks Polarized networks, diameter, and synchronizability of networks

2006-04-12

arxiv.org/abs/cond-mat/0604295v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 5 figures

Scientific paper

Previous research claimed or disclaimed the role of a small diameter in the synchronization of a network of coupled dynamical systems. We investigate this connection and show that it is two folds. We first construct two classes of networks, the polarized networks and the random networks with a fixed diameter, which exhibit very different synchronizability. This shows that the diameter itself is insufficient to determine the synchronizability of networks. Secondly, we derive analytic estimates on the synchronizability of networks in terms of the diameter, and find that a larger size of network admits of a more flexible synchronizability. The analysis is confirmed by numerical results.

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