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CLC number: O155; TP11

On-line Access: 2020-06-12

Received: 2019-03-08

Revision Accepted: 2019-06-23

Crosschecked: 2019-08-09

Cited: 0

Clicked: 704

Citations:  Bibtex RefMan EndNote GB/T7714


Wei-gang Sun


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Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.6 P.931-938


Coherence analysis and Laplacian energy of recursive trees with controlled initial states

Author(s):  Mei-du Hong, Wei-gang Sun, Su-yu Liu, Teng-fei Xuan

Affiliation(s):  School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China

Corresponding email(s):   wgsun@hdu.edu.cn

Key Words:  Consensus, Network coherence, Laplacian energy

Mei-du Hong, Wei-gang Sun, Su-yu Liu, Teng-fei Xuan. Coherence analysis and Laplacian energy of recursive trees with controlled initial states[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(6): 931-938.

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A1 - Mei-du Hong
A1 - Wei-gang Sun
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DOI - 10.1631/FITEE.1900133

We study the consensus of a family of recursive trees with novel features that include the initial states controlled by a parameter. The consensus problem in a linear system with additive noises is characterized as network coherence, which is defined by a Laplacian spectrum. Based on the structures of our recursive treelike model, we obtain the recursive relationships for Laplacian eigenvalues in two successive steps and further derive the exact solutions of first- and second-order coherences, which are calculated by the sum and square sum of the reciprocal of all nonzero Laplacian eigenvalues. For a large network size N, the scalings of the first- and second-order coherences are lnN and N$, respectively. The smaller the number of initial nodes, the better the consensus bears. Finally, we numerically investigate the relationship between network coherence and laplacian energy, showing that the first- and second-order coherences increase with the increase of laplacian energy at approximately exponential and linear rates, respectively.





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