TUMOR CELL GROWTH SUBJECTED TO CORRELATED NOISES AND TIME DELAY

2016 ◽  
Vol 16 (02) ◽  
pp. 1650015
Author(s):  
Y. L. FENG ◽  
L. L. GAO ◽  
Y. F. LIU ◽  
M. ZHANG ◽  
J. M. DONG
Keyword(s):  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Cell Population ◽  
First Passage Time ◽  
Planck Equation ◽  
Tumor Cell Growth ◽  
Tumor Cell Population ◽  
Correlation Strength ◽  
Correlated Noises

The tumor cell growth with time-delayed feedback driven by correlated noises under the immune surveillance are investigated within an anti-tumor model. The effects of the noise correlation strength and time delay on the stationary probability distribution, the average tumor cell population and the mean first passage time (MFPT) are analyzed in detail based on the delay Fokker–Planck equation. The effects of the correlation strength and time delay could play the same role in the average tumor cell population, but play opposite role in the MFPT. In addition, the role of the correlation strength and time delay for different activation thresholds of immune system is explored.

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.

Stochastic resonance in a time-delayed tumor cell growth system driven by additive and multiplicative noises

2018 ◽  
Vol 32 (22) ◽  
pp. 1850259 ◽  
Author(s):  
Gang Zhang ◽  
Jiabei Shi ◽  
Tianqi Zhang
Keyword(s):  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
State Theory ◽  
Periodic Signal ◽  
Tumor Cell Growth ◽  
System Parameters ◽  
Growth System

In this paper, the stochastic resonance (SR) phenomenon in a time-delayed tumor cell growth system subjected to a multiplicative periodic signal, the multiplicative and additive noise is investigated. By applying the small time-delay method and two-state theory, the expressions of the mean first-passage time (MFPT) and signal-to-noise ratio (SNR) are obtained, then, the impacts of time delay, noise intensities and system parameters on the MFPT and SNR are discussed. Simulation results show that the multiplicative and additive noise always weaken the SR effect; while time delay plays a key role in motivating the SR phenomenon when noise intensities take a small value, it will restrain SR phenomenon when noise intensities take a large value; the cycle radiation amplitude always plays a positive role in stimulating the SR phenomenon, while, system parameters play different roles in motivating or suppressing SR under the different conditions of noise intensities.

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.

DYNAMICAL PROPERTIES OF AN ANTI-TUMOR CELL GROWTH SYSTEM IN THE PRESENCE OF DELAY AND CORRELATED NOISES

2009 ◽  
Vol 23 (13) ◽  
pp. 1651-1661 ◽  
Author(s):  
CHUN-HUA ZENG ◽  
CHONG-WEI XIE
Keyword(s):  
Relaxation Time ◽  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Small Time ◽  
Correlated Noise ◽  
Tumor Cell Growth ◽  
Stationary Probability Distribution ◽  
Growth System ◽  
Dynamical Properties

We study dynamical properties of an anti-tumor cell growth system in the presence of time delay and correlations between multiplicative and additive white noise. Using the small time delay approximation, the Novikov theorem and Fox approach, the stationary probability distribution (SPD) is obtained. Based on the SPD, the expressions of the normalized correlation function C(s) and the associated relaxation time Tc are derived by means of Stratonovich decoupling ansatz. Based on numerical computations, we find the following: (i) The SPD exhibits one-peak → two-peaks → one-peak phase transitions as the correlation intensity λ varies. (ii) The relaxation time Tc exhibits a one-peak structure for negatively correlated noise (λ<0), however for positively correlated noise (λ>0), the relaxation time Tc decreases monotonously. (iii) The effects of the delay time τ on Tc and C(s) are entirely the same for λ<0 and for λ>0, i.e. τ enhances the fluctuation decay of the population of tumor cells.

INFLUENCE OF TIME DELAY ON STOCHASTIC RESONANCE IN THE TUMOR CELL GROWTH MODEL

2008 ◽  
Vol 22 (28) ◽  
pp. 2759-2767 ◽  
Author(s):  
JIANCHUN CAI ◽  
DONGCHENG MEI
Keyword(s):  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Stochastic Resonance ◽  
Growth Model ◽  
Delay Time ◽  
Noise Intensity ◽  
Tumor Cell Growth ◽  
Tumor Cell Growth Model ◽  
Cell Growth Model

We study the effects of time delay on stochastic resonance (SR) in the tumor cell growth model driven by two coupled noises and a weak external periodic signal. Under the condition of small delay time, we obtained the signal-to-noise ratio (SNR) R SNR from the quasi-steady-state probability distribution function through the adiabatic elimination method and the SR theory about a two-state transition. By the numerical computations, we discussed the effects of the delay time τ on the SNR as a function of the multiplicative noise intensity D, the additive noise intensity α and the cross-correlated strength λ respectively. The appearance of a peak in these curves represents the SR phenomenon. It is found that with the increase of τ, the SR is suppressed in the D–R SNR plot and weakened in the α–R SNR plot. However, the SR is strengthened with the increase of τ in the λ–R SNR plot.

scholarly journals Structural and stereochemical studies of potent inhibitors of glucosylceramide synthase and tumor cell growth.

1995 ◽  
Vol 36 (3) ◽  
pp. 611-621
Author(s):  
A Abe ◽  
N S Radin ◽  
J A Shayman ◽  
L L Wotring ◽  
R E Zipkin ◽  
...  
Keyword(s):  
Cell Growth ◽  
Tumor Cell ◽  
Tumor Cell Growth ◽  
Glucosylceramide Synthase
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