FIRST-ORDER NETWORK COHERENCE AND EIGENTIME IDENTITY ON THE WEIGHTED CAYLEY NETWORKS

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750049 ◽  
Author(s):  
MEIFENG DAI ◽  
XIAOQIAN WANG ◽  
YUE ZONG ◽  
JIAHUI ZOU ◽  
YUFEI CHEN ◽  
...  
Keyword(s):  
First Passage Time ◽  
Analytical Formula ◽  
Passage Time ◽  
Small Degree ◽  
Network Size ◽  
Mean First Passage Time ◽  
Weight Factor ◽  
First Passage ◽  
First Order ◽  
Definition Of

In this paper, we first study the first-order network coherence, characterized by the entire mean first-passage time (EMFPT) for weight-dependent walk, on the weighted Cayley networks with the weight factor. The analytical formula of the EMFPT is obtained by the definition of the EMFPT. The obtained results show that the scalings of first-order coherence with network size obey four laws along with the range of the weight factor. Then, we study eigentime identity quantifying as the sum of reciprocals of all nonzero normalized Laplacian eigenvalues on the weighted Cayley networks with the weight factor. We show that all their eigenvalues can be obtained by calculating the roots of several small-degree polynomials defined recursively. The obtained results show that the scalings of the eigentime identity on the weighted Cayley networks obey two laws along with the range of the weight factor.

Mean first-passage time on a family of small-world treelike networks

2014 ◽  
Vol 25 (03) ◽  
pp. 1350097 ◽  
Author(s):  
Long Li ◽  
Weigang Sun ◽  
Guixiang Wang ◽  
Guanghui Xu
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Small World ◽  
Passage Time ◽  
Network Size ◽  
Mean First Passage Time ◽  
First Passage ◽  
Initial Node ◽  
Laplacian Spectra ◽  
Two Parameters

In this paper, we obtain exact scalings of mean first-passage time (MFPT) of random walks on a family of small-world treelike networks formed by two parameters, which includes three kinds. First, we determine the MFPT for a trapping problem with an immobile trap located at the initial node, which is defined as the average of the first-passage times (FPTs) to the trap node over all possible starting nodes, and it scales linearly with network size N in large networks. We then analytically obtain the partial MFPT (PMFPT) which is the mean of FPTs from the trap node to all other nodes and show that it increases with N as N ln N. Finally we establish the global MFPT (GMFPT), which is the average of FPTs over all pairs of nodes. It also grows with N as N ln N in the large limit of N. For these three kinds of random walks, we all obtain the analytical expressions of the MFPT and they all increase with network parameters. In addition, our method for calculating the MFPT is based on the self-similar structure of the considered networks and avoids the calculations of the Laplacian spectra.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

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.

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