Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

2012 ◽  
Vol 21 (3) ◽  
pp. 038901 ◽  
Author(s):  
Jing-Yuan Zhang ◽  
Wei-Gang Sun ◽  
Guan-Rong Chen
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Exact Scaling

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.

MEAN FIRST PASSAGE TIME OF RANDOM WALKS ON THE GENERALIZED PSEUDOFRACTAL WEB

2013 ◽  
Vol 27 (10) ◽  
pp. 1350070 ◽  
Author(s):  
LONG LI ◽  
WEIGANG SUN ◽  
JING CHEN ◽  
GUIXIANG WANG
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Scaling Exponent ◽  
Mean First Passage Time ◽  
Initial State ◽  
First Passage ◽  
Subsequent Step ◽  
Power Law Function ◽  
Exact Scaling

In this paper, we study the scaling for mean first passage time (MFPT) of random walks on the generalized pseudofractal web (GPFW) with a trap, where an initial state is transformed from a triangle to a r-polygon and every existing edge gives birth to finite nodes in the subsequent step. We then obtain an analytical expression and an exact scaling for the MFPT, which shows that the MFPT grows as a power-law function in the large limit of network order. In addition, we determine the exponent of scaling efficiency characterizing the random walks, with the exponent less than 1. The scaling exponent of the MFPT is same for the initial state of the web being a polygon with finite nodes. This method could be applied to other fractal networks.

scholarly journals Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Zhongtuan Zheng ◽  
Gaoxi Xiao ◽  
Guoqiang Wang ◽  
Guanglin Zhang ◽  
Kaizhong Jiang
Keyword(s):  
Complex Networks ◽  
Random Walks ◽  
First Passage Time ◽  
Network Models ◽  
Passage Time ◽  
Main Role ◽  
Mean First Passage Time ◽  
Eigenvalues And Eigenvectors ◽  
First Passage ◽  
The Mean

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

scholarly journals Mean first-passage time of a tumor cell growth system with time delay and colored cross-correlated noises excitation

2017 ◽  
Vol 37 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Shenghong Li ◽  
Yong Huang
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Tumor Cell Growth ◽  
First Passage ◽  
Growth System ◽  
The Mean ◽  
Correlated Noises

In this paper, the mean first-passage time of a delayed tumor cell growth system driven by colored cross-correlated noises is investigated. Based on the Novikov theorem and the method of probability density approximation, the stationary probability density function is obtained. Then applying the fastest descent method, the analytical expression of the mean first-passage time is derived. Finally, effects of different kinds of delays and noise parameters on the mean first-passage time are discussed thoroughly. The results show that the time delay included in the random force, additive noise intensity and multiplicative noise intensity play a positive role in the disappearance of tumor cells. However, the time delay included in the determined force and the correlation time lead to the increase of tumor cells.

Scaling of average receiving time on double-weighted polygon networks

2021 ◽  
Author(s):  
Xiaoyan Li ◽  
Yu Sun
Keyword(s):  
Iterative Method ◽  
Path Length ◽  
First Passage Time ◽  
Passage Time ◽  
Traffic Networks ◽  
Mean First Passage Time ◽  
First Passage ◽  
Specific Calculation ◽  
Calculation Process ◽  
The Mean

In this paper, we introduce a class of double-weighted polygon networks with two different meanings of weighted factors [Formula: see text] and [Formula: see text], which represent path-difficulty and path-length, respectively, based on actual traffic networks. Picking an arbitrary node from the hub nodes set as the trap node, and the double-weighted polygon networks are divided into [Formula: see text] blocks by combining with the iterative method. According to biased random walks, the calculation expression of average receiving time (ART) of any polygon networks is given by using the intermediate quantity the mean first-passage time (MFPT), which is applicable to any [Formula: see text] ([Formula: see text]) polygon networks. What is more, we display the specific calculation process and results of ART of the double-weighted quadrilateral networks, indicating that ART grows exponentially with respect to the networks order and the exponent is [Formula: see text] which grows with the product of [Formula: see text]. When [Formula: see text] increases, ART increases linearly ([Formula: see text]) or sublinearly ([Formula: see text]) with the size of networks, and the smaller value of [Formula: see text], the higher transportation efficiency.

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