scholarly journals Transient properties of a tumor cell growth system driven by color Gaussian noises: Mean first-passage time

2008 ◽  
Vol 57 (3) ◽  
pp. 1375
Author(s):  
Wang Can-Jun ◽  
Wei Qun ◽  
Zheng Bao-Bing ◽  
Mei Dong-Cheng
Keyword(s):  
Cell Growth ◽  
Tumor Cell ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Tumor Cell Growth ◽  
First Passage ◽  
Growth System

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.

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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