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Research On Random Walk And Hitting Time Of A Kind Of Sierpinski Extended Networks

Posted on:2024-03-11Degree:MasterType:Thesis
Country:ChinaCandidate:X B LiuFull Text:PDF
GTID:2530307127993639Subject:Mathematics
Abstract/Summary:PDF Full Text Request
In this dissertation,we are concerned with the random walk on a kind of Sierpinski extension network,which is derived from the Sierpinski Gasket.Therefore,we call it the Sierpinski extension network.The full text is divided into four parts: the background knowledge of complex networks,the random walk on the Sierpinski network,the hitting time of the Half Sierpinski network,and the random walk problem on the Joint Sierpinski network.In the first part,we mainly explain the background of complex networks,the research context,innovation of this dissertation and the related knowledge and concepts involved in this paper.In the second part,we describe the construction process of the Sierpinski network model.According to the characteristics of network structure,the jumping probability and global hitting time of some connecting nodes are derived on the network by using the method of model block.The exact formula of the total hitting time and the average trapping time are obtained with the trap node.In the third part,we introduce the random walk on Half Sierpinski network,which is obtained by cutting the network described in the last part along the vertical segmentation line,and derive the exact expression of the total hitting time and the average trapping time.In addition,the influence of cutting behavior on the average trapping time is analyzed by means of numerical simulation on the network.Finally,in the fourth part,we construct the Joint Sierpinski network,which is generated by embedding the Sierpinski network into the model variable.The analytical expression of the total hitting time and the average trapping time in the general Joint Sierpinski network was calculated.At the same time,we give and study the five model variables and their derived networks.It is found that the average trapping time is determined by the generation and model variables.In addition,the exact expressions of the total hitting time and the average trapping time are calculated for the five derived Joint Sierpinski network models.
Keywords/Search Tags:random walk, Sierpinski extended network, hitting time, vertical cutting
PDF Full Text Request
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