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.

The mean first passage time and stochastic resonance in gene transcriptional system with time delay

2016 ◽  
Vol 30 (11) ◽  
pp. 1650067 ◽  
Author(s):  
Y. L. Feng ◽  
J. Zhu ◽  
M. Zhang ◽  
L. L. Gao ◽  
Y. F. Liu ◽  
...  
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Noise Correlation ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Correlation Strength

In this paper, the gene transcriptional dynamics driven by correlated noises are investigated, where the time delay for the synthesis of transcriptional factor is introduced. The effects of the noise correlation strength and time delay on the stationary probability distribution (SPD), the mean first passage time and the stochastic resonance (SR) are analyzed in detail based on the delay Fokker–Planck equation. It is found that both the time delay and noise correlation strength play important roles in the bistable transcriptional system. The effect of the correlation strength reduces but the time delay enhances the mean first passage time (MFPT). Finally, the SR for this gene transcriptional system is found to be enhanced by the time delay.

MEAN FIRST-PASSAGE TIME OF A TUMOR CELL GROWTH SYSTEM SUBJECTED TO A COLORED MULTIPLICATIVE NOISE AND A WHITE ADDITIVE NOISE WITH COLORED CROSS-CORRELATED NOISES

2007 ◽  
Vol 21 (13) ◽  
pp. 789-797 ◽  
Author(s):  
CAN-JUN WANG ◽  
QUN WEI ◽  
DONG-CHENG MEI
Keyword(s):  
Cell Growth ◽  
Tumor Cell ◽  
Correlation Time ◽  
Multiplicative Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Tumor Cell Growth ◽  
First Passage ◽  
Growth System

The transient properties of a tumor cell growth system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are colored with different correlation times τ1 and τ2. The explicit expression of the mean first-passage time (MFPT) of the tumor cell growth system is obtained. The numerical computations show that the MFPT decreases with increases in D (multiplicative colored intensity) and α (additive white intensity). However, τ1 (correlation time of the multiplicative colored noise) can only linearly enhance the MFPT. It is interesting that the curves of the MFPT appears a peak structure as λ (correlation intensity) and τ2 (coupling correlation time) increases; namely, the MFPT can be enhanced for the small value of λ and τ2 and reduced for the large value of λ and the τ2.

The mean first-passage time in simplified FitzHugh–Nagumo neural model driven by correlated non-Gaussian noise and Gaussian noise

2018 ◽  
Vol 32 (28) ◽  
pp. 1850339 ◽  
Author(s):  
Yong-Feng Guo ◽  
Bei Xi ◽  
Fang Wei ◽  
Jian-Guo Tan
Keyword(s):  
Gaussian Noise ◽  
Noise Intensity ◽  
First Passage Time ◽  
Neural Model ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Model Driven ◽  
The Mean ◽  
Non Gaussian

In this paper, the mean first-passage time (MFPT) in simplified FitzHugh–Nagumo (FHN) neural model driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise is studied. Firstly, using the path integral approach and the unified colored-noise approximation (UCNA), the analytical expression of the stationary probability distribution (SPD) is derived, and the validity of the approximation method employed in the derivation is checked by performing numerical simulation. Secondly, the expression of the MFPT of the system is obtained by applying the definition and the steepest-descent method. Finally, the effects of the multiplicative noise intensity D, the additive noise intensity Q, the noise correlation time [Formula: see text], the cross-correlation strength [Formula: see text] and the non-Gaussian noise deviation parameter q on the MFPT are discussed.

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