The relationship between synchronization and percolation for regular networks

Zhe Li, Tao Ren, Yanjie Xu and Jianyu Jin

Physica A: Statistical Mechanics and its Applications, 2018, vol. 492, issue C, 375-381

Abstract: Synchronization and percolation are two essential phenomena in complex dynamical networks. They have been studied widely, but previously treated as unrelated. In this paper, the relationship between synchronization and percolation are revealed for regular networks. Firstly, we discovered a bridge between synchronization and percolation by using the eigenvalues of the Laplacian matrix to describe the synchronizability and using the eigenvalues of the adjacency matrix to describe the percolation threshold. Then, we proposed a method to find the relationship for regular networks based on the topology of networks. Particularly, if the degree distribution of the network is subject to delta function, we show that only the eigenvalues of the adjacency matrix need to be calculated. Finally, several examples are provided to demonstrate how to apply our proposed method to discover the relationship between synchronization and percolation for regular networks.

Keywords: Complex networks; Synchronizability; Percolation threshold; Regular networks (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:492:y:2018:i:c:p:375-381

DOI: 10.1016/j.physa.2017.10.003

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