期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 50, 期 1, 页码 190-200出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2018.2868124
关键词
Distributed average consensus; Gaussian white noise; network coherence; resistance distance; scale-free network; small-world network
类别
资金
- National Natural Science Foundation of China [61872093]
- NSF [CNS-1527287, CNS-1553340]
The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices arc subject to white noise. We focus on the coherence of networks characterized in terms of the H-2-norm, which quantifies how closely the agents track the consensus value. We first provide a lower bound of coherence of a network in terms of its average degree, which is independent of the network order. We then study the coherence of some sparse, scale-free real-world networks, which approaches a constant. We also study numerically the coherence of Barabisi-Albert networks and high-dimensional random Apollonian networks, which also converges to a constant when the networks grow. Finally, based on the connection of coherence and the Kirchhoff index, we study analytically the coherence of two deterministically growing sparse networks and obtain the exact expressions, which tend to small constants. Our results indicate that the effect of noise on the consensus dynamics in power-law networks is negligible. We argue that scale-free topology, together with loopy structure, is responsible for the strong robustness with respect to noisy consensus dynamics in power-law networks.
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