Consensus on de Bruijn graphs |
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Authors: | G Yan Z -Q Fu G Chen |
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Affiliation: | (1) Department of Electronic Science and Technology, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China;(2) Centre for Chaos and Complex Networks and Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P.R. China |
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Abstract: | We study the consensus dynamics with or without time-delays on directed and undirected de Bruijn graphs. Our results show
that consensus on an undirected de Bruijn graph has a lower converging speed and larger time-delay tolerance in comparison
with that on an undirected scale-free network. Although there is not much difference between the eigenvalue ratios of the
two undirected networks, we found that their dynamical properties are remarkably different; consequently, it is seemingly
more informative to consider the second smallest and the largest eigenvalues separately rather than considering their ratio
in the study of synchronization of a coupled oscillators network. Moreover, our study on directed de Bruijn graphs reveals
that properly setting directions on edges can improve the converging speed and time-delay tolerance simultaneously. |
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Keywords: | PACS" target="_blank">PACS 89 75 -k Complex systems 05 45 Xt Synchronization coupled oscillators |
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