scholarly journals Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees

2021 ◽  
Vol 5 (4) ◽  
pp. 184
Author(s):  
Long Gao ◽  
Junhao Peng ◽  
Chunming Tang
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Exact Result ◽  
Passage Time ◽  
Target Site ◽  
Mean First Passage Time ◽  
First Passage ◽  
Scale Free ◽  
Global Mean ◽  
Biased Random Walks

First-passage processes on fractals are of particular importance since fractals are ubiquitous in nature, and first-passage processes are fundamental dynamic processes that have wide applications. The global mean first-passage time (GMFPT), which is the expected time for a walker (or a particle) to first reach the given target site while the probability distribution for the position of target site is uniform, is a useful indicator for the transport efficiency of the whole network. The smaller the GMFPT, the faster the mass is transported on the network. In this work, we consider the first-passage process on a class of fractal scale-free trees (FSTs), aiming at speeding up the first-passage process on the FSTs. Firstly, we analyze the global mean first-passage time (GMFPT) for unbiased random walks on the FSTs. Then we introduce proper weight, dominated by a parameter w(w>0), to each edge of the FSTs and construct a biased random walks strategy based on these weights. Next, we analytically evaluated the GMFPT for biased random walks on the FSTs. The exact results of the GMFPT for unbiased and biased random walks on the FSTs are both obtained. Finally, we view the GMFPT as a function of parameter w and find the point where the GMFPT achieves its minimum. The exact result is obtained and a way to optimize and speed up the first-passage process on the FSTs is presented.

Mean first passage time on a family of weighted directed hierarchical scale-free networks

2019 ◽  
Vol 33 (16) ◽  
pp. 1950179 ◽  
Author(s):  
Yu Gao ◽  
Zikai Wu
Keyword(s):  
Random Walks ◽  
Numerical Solutions ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Scale Free ◽  
Weight Parameter ◽  
Scale Free Networks ◽  
Hierarchical Scale

Random walks on binary scale-free networks have been widely studied. However, many networks in real life are weighted and directed, the dynamic processes of which are less understood. In this paper, we firstly present a family of directed weighted hierarchical scale-free networks, which is obtained by introducing a weight parameter [Formula: see text] into the binary (1, 3)-flowers. Besides, each pair of nodes is linked by two edges with opposite direction. Secondly, we deduce the mean first passage time (MFPT) with a given target as a measure of trapping efficiency. The exact expression of the MFPT shows that both its prefactor and its leading behavior are dependent on the weight parameter [Formula: see text]. In more detail, the MFPT can grow sublinearly, linearly and superlinearly with varied [Formula: see text]. Last but not least, we introduce a delay parameter p to modify the transition probability governing random walk. Under this new scenario, we also derive the exact solution of the MFPT with the given target, the result of which illustrates that the delay parameter p can only change the coefficient of the MFPT and leave the leading behavior of MFPT unchanged. Both the analytical solutions of MFPT in two distinct scenarios mentioned above agree well with the corresponding numerical solutions. The analytical results imply that we can get desired transport efficiency by tuning weight parameter [Formula: see text] and delay parameter p. This work may help to advance the understanding of random walks in general directed weighted scale-free networks.

scholarly journals Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices

2010 ◽  
Vol 81 (3) ◽  
Author(s):  
Zhongzhi Zhang ◽  
Bin Wu ◽  
Hongjuan Zhang ◽  
Shuigeng Zhou ◽  
Jihong Guan ◽  
...  
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Laplacian Matrices ◽  
Global Mean

Calculations of first passage time of delayed tree-like networks

2015 ◽  
Vol 29 (28) ◽  
pp. 1550200
Author(s):  
Shuai Wang ◽  
Weigang Sun ◽  
Song Zheng
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
The Novel ◽  
Mean First Passage Time ◽  
First Passage ◽  
Initial Node ◽  
Network Parameters ◽  
Self Similar ◽  
The Mean

In this paper, we study random walks in a family of delayed tree-like networks controlled by two network parameters, where an immobile trap is located at the initial node. The novel feature of this family of networks is that the existing nodes have a time delay to give birth to new nodes. By the self-similar network structure, we obtain exact solutions of three types of first passage time (FPT) measuring the efficiency of random walks, which includes the mean receiving time (MRT), mean sending time (MST) and mean first passage time (MFPT). The obtained results show that the MRT, MST and MFPT increase with the network parameters. We further show that the values of MRT, MST and MFPT are much shorter than the nondelayed counterpart, implying that the efficiency of random walks in delayed trees is much higher.

scholarly journals Mean first-passage time for random walks on the T-graph

2009 ◽  
Vol 11 (10) ◽  
pp. 103043 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yuan Lin ◽  
Shuigeng Zhou ◽  
Bin Wu ◽  
Jihong Guan
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage

scholarly journals Mean first-passage time for random walks on undirected networks

2011 ◽  
Vol 84 (4) ◽  
pp. 691-697 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Alafate Julaiti ◽  
Baoyu Hou ◽  
Hongjuan Zhang ◽  
Guanrong Chen
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage
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