Mean First-Passage Time on Scale-Free Networks Based on Rectangle Operation

The mean first-passage time of random walks on a network has been extensively applied in the theory and practice of statistical physics, and its application effects depend on the behavior of first-passage time. Here, we firstly define a graphic operation, namely, rectangle operation, for generating a scale-free network. In this paper, we study the topological structures of our network obtained from the rectangle operation, including degree distribution, clustering coefficient, and diameter. And then, we also consider the characteristic quantities related to the network, including Kirchhoff index and mean first-passage time, where these characteristic quantities can not only be used to evaluate the properties of our network, but also have remarkable applications in science and engineering.

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

Modern Physics Letters B ◽

10.1142/s0217984919501793 ◽

2019 ◽

Vol 33 (16) ◽

pp. 1950179 ◽

Cited By ~ 3

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.

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Spontaneous Activity Induced by Gaussian Noise in the Network-Organized FitzHugh-Nagumo Model

Neural Plasticity ◽

10.1155/2020/6651441 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Qianqian Zheng ◽

Jianwei Shen ◽

Yong Xu

Keyword(s):

Gaussian Noise ◽

Short Term Memory ◽

First Passage Time ◽

Passage Time ◽

Clustering Coefficient ◽

Toggle Switch ◽

Mean First Passage Time ◽

Short Term ◽

First Passage ◽

Term Memory

In this paper, we show some dynamical and biological mechanisms of the short-term memory (the fixed point attractor) through the toggle switch in the FitzHugh-Nagumo model (FN). Firstly, we obtain the bistable conditions, show the effect of Gaussian noise on the toggle switch, and explain the short-term memory’s switch mechanism by mean first passage time (MFPT). Then, we obtain a Fokker-Planck equation and illustrate the meaning of the monostable and bistable state in the short-term memory. Furthermore, we study the toggle switch under the interaction of network and noise. Meanwhile, we show that network structure and noise play a vital role in the toggle switch based on network mean first passage time (NMFPT). And we illustrate that the modest clustering coefficient and noise are necessary to maintain memories. Finally, the numerical simulation shows that the analytical results agree with it.

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Exact solution for mean first-passage time on a pseudofractal scale-free web

Physical Review E ◽

10.1103/physreve.79.021127 ◽

2009 ◽

Vol 79 (2) ◽

Cited By ~ 93

Author(s):

Zhongzhi Zhang ◽

Yi Qi ◽

Shuigeng Zhou ◽

Wenlei Xie ◽

Jihong Guan

Keyword(s):

Exact Solution ◽

First Passage Time ◽

Passage Time ◽

Mean First Passage Time ◽

First Passage ◽

Scale Free

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Volatilities analysis of first-passage time and first-return time on a small-world scale-free network

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2016/03/033103 ◽

2016 ◽

Vol 2016 (3) ◽

pp. 033103 ◽

Cited By ~ 1

Author(s):

Junhao Peng

Keyword(s):

First Passage Time ◽

Small World ◽

Return Time ◽

Passage Time ◽

Scale Free Network ◽

First Passage ◽

Scale Free ◽

Free Network ◽

First Return Time

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

Fractal and Fractional ◽

10.3390/fractalfract5040184 ◽

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.

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