The trapping problem of the weighted scale-free treelike networks for two kinds of biased walks

被引:16
作者
Dai, Meifeng [1 ]
Zong, Yue [1 ]
He, Jiaojiao [1 ]
Sun, Yu [1 ]
Shen, Chunyu [2 ]
Su, Weiyi [3 ]
机构
[1] Jiangsu Univ, Inst Appl Syst Anal, Zhenjiang 212013, Jiangsu, Peoples R China
[2] Jiangsu Univ, Nonlinear Sci Res Ctr, Zhenjiang 212013, Jiangsu, Peoples R China
[3] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
基金
中国国家自然科学基金;
关键词
1ST-PASSAGE TIMES; SYNCHRONIZATION; FAMILY;
D O I
10.1063/1.5045829
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
It has been recently reported that trapping problem can characterize various dynamical processes taking place on complex networks. However, most works focused on the case of binary networks, and dynamical processes on weighted networks are poorly understood. In this paper, we study two kinds of biased walks including standard weight-dependent walk and mixed weight-dependent walk on the weighted scale-free treelike networks with a trap at the central node. Mixed weight-dependent walk including non-nearest neighbor jump appears in many real situations, but related studies are much less. By the construction of studied networks in this paper, we determine all the eigenvalues of the fundamental matrix for two kinds of biased walks and show that the largest eigenvalue has an identical dominant scaling as that of the average trapping time (ATT). Thus, we can obtain the leading scaling of ATT by a more convenient method and avoid the tedious calculation. The obtained results show that the weight factor has a significant effect on the ATT, and the smaller the value of the weight factor, the more efficient the trapping process is. Comparing the standard weight-dependent walk with mixed weight-dependent walk, although next-nearest-neighbor jumps have no main effect on the trapping process, they can modify the coefficient of the dominant term for the ATT. Published by AIP Publishing.
引用
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页数:10
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