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Manipulating directed networks for better synchronization

Video abstract for the article 'Manipulating directed networks for better synchronization ' by An Zeng, Linyuan Lü and Tao Zhou (An Zeng et al 2012 New J. Phys. 14 083006). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/14/8/083006/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. Synchronization is an important dynamical process in many systems. As real systems are frequently manipulated by growing out new connections and eliminating redundant connections, we focus on the link manipulating method to enhance synchronizability. Since the complex value emerges in eigenvectors when the Laplacian matrix is asymmetrical, the existing spectral manipulating method cannot be directly applied to directed networks. We therefore employ the PageRank algorithm to design a centrality-based manipulating (CBM) method to enhance synchronizability of directed networks when a small number of connections are changed. Main results. We apply the CBM method to enhance synchronizability of some modeled networks by adding and removing links. Interestingly, the CBM method can be also used to rewire the network and the resultant synchronizability can be very close to the optimal case from the evolutionary optimization algorithm and theoretical analysis. The numerical simulations on the Kuramoto model further demonstrate that our method has advantages in shortening the convergence time to synchronization on directed networks. Wider implications. Our method is widely applicable for many real systems involving a synchronized process such as power grid, wireless communication system, opinion formation and so on. In some specific systems e.g. ecosystems and neuron systems, synchronization should be inhibited in some cases. In such situations, the inverted CBM method can be applied to decrease the synchronizability.