EFFECTS OF CORRELATED NOISES IN A SATURATION LASER MODEL

2006 ◽  
Vol 20 (23) ◽  
pp. 1481-1488 ◽  
Author(s):  
P. ZHU ◽  
S. B. CHEN ◽  
D. C. MEI
Keyword(s):  
Steady State ◽  
Intensity Fluctuation ◽  
Laser System ◽  
Planck Equation ◽  
Steady State Probability ◽  
Multiplicative Noises ◽  
Analytic Expressions ◽  
Laser Model ◽  
Correlation Strength ◽  
Correlated Noises

The effects of correlations between additive and multiplicative noises in a saturation laser model are investigated. The approximative Fokker–Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. Our results indicate that: (i) For the laser being operated above threshold, the correlation strength λ reduces the intensity fluctuation; (ii) For the laser being operated near threshold and below threshold, the correlation strength λ enhances the intensity fluctuation.

STATISTICAL FLUCTUATION IN A SATURATION LASER MODEL WITH CROSS-CORRELATIONS BETWEEN THE REAL AND IMAGINARY PARTS OF QUANTUM NOISE

2010 ◽  
Vol 24 (24) ◽  
pp. 4881-4888
Author(s):  
Y. H. LI ◽  
C. S. MA ◽  
D. C. MEI
Keyword(s):  
Quantum Noise ◽  
Laser System ◽  
Planck Equation ◽  
Phase Method ◽  
Statistical Fluctuation ◽  
Stationary Probability Distribution ◽  
The Real ◽  
Analytic Expressions ◽  
Cross Correlations ◽  
Laser Model

We study the effects of cross-correlations between the real and imaginary parts of quantum noise on the intensity fluctuation of a saturation laser model. By virtue of the locked phase method,we derived an approximate Fokker–Planck equation and analytic expressions of the stationary probability distribution function (SPD) of the laser system. Based on the SPD, the mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that the correlation strength of the cross-correlations between the real and imaginary parts of quantum noise increases the intensity fluctuations.

STATISTICAL PROPERTIES OF INTENSITY FLUCTUATION OF SATURATION LASER MODEL DRIVEN BY CROSS-CORRELATED ADDITIVE AND MULTIPLICATIVE NOISES

2010 ◽  
Vol 24 (14) ◽  
pp. 2175-2188 ◽  
Author(s):  
PING ZHU ◽  
YI JIE ZHU
Keyword(s):  
Probability Distribution ◽  
Cross Correlation ◽  
Laser Intensity ◽  
Laser System ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Model Driven ◽  
Multiplicative Noises ◽  
Laser Model ◽  
The Stability

Statistical properties of the intensity fluctuation of a saturation laser model driven by cross-correlation additive and multiplicative noises are investigated. Using the Novikov theorem and the projection operator method, we obtain the analytic expressions of the stationary probability distribution Pst(I), the relaxation time Tc, and the normalized variance λ2(0) of the system. By numerical computation, we discussed the effects of the cross-correlation strength λ, the cross-correlation time τ, the quantum noise intensity D, and the pump noise intensity Q for the fluctuation of the laser intensity. Above the threshold, λ weakens the stationary probability distribution, speeds up the startup velocity of the laser system from start status to steady work, and attenuates the stability of laser intensity output; however, τ strengthens the stationary probability distribution and strengths the stability of laser intensity output; when λ < 0, τ speeds up the startup; on the contrast, when λ > 0, τ slows down the startup. D and Q make the relaxation time exhibit extremum structure, that is, the startup time possesses the least values. At the threshold, τ cannot generate the effects for the saturation laser system, λ expedites the startup velocity and weakens the stability of laser intensity output. Below threshold, the effects of λ and τ not only relate to λ and τ, but also relate to other parameters of the system.

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.

Colored correlated multiplicative and additive Gaussian colored noises-induced transition of a piecewise nonlinear bistable model

2017 ◽  
Vol 31 (28) ◽  
pp. 1750256 ◽  
Author(s):  
Yong-Feng Guo ◽  
Ya-Jun Shen ◽  
Bei Xi ◽  
Jian-Guo Tan
Keyword(s):  
Steady State ◽  
Correlation Time ◽  
Noise Intensity ◽  
Cross Correlation ◽  
Colored Noise ◽  
Nonlinear Phenomena ◽  
Steady State Probability ◽  
Model Driven ◽  
Correlation Strength ◽  
The Cross

In this paper, we investigate the steady-state properties of a piecewise nonlinear bistable model driven by multiplicative and additive Gaussian colored noises with colored cross-correlation. Using the unified colored noise approximation, we derive the analytical expression of the steady-state probability density (SPD) function. Then the effects of colored correlated Gaussian colored noises on SPD are presented. According to the research results, it is found that there appear some new nonlinear phenomena in this system. The multiplicative colored noise intensity, the additive colored noise intensity and the cross-correlation strength between noises can induce the transition. However, the transition cannot be induced by the auto-correlation time of multiplicative and additive Gaussian colored noises as well as the cross-correlation time between noises.

INFLUENCE OF CORRELATED NOISES ON GROWTH OF A TUMOR IN A MODIFIED VERHULST MODEL

2006 ◽  
Vol 06 (04) ◽  
pp. L349-L358 ◽  
Author(s):  
WEI-RONG ZHONG ◽  
YUAN-ZHI SHAO ◽  
ZHEN-HUI HE
Keyword(s):  
Tumor Growth ◽  
Tumor Cells ◽  
Multiplicative Noise ◽  
Stable State ◽  
Logistic Growth ◽  
Tumor Treatment ◽  
Steady State Probability ◽  
Multiplicative Noises ◽  
The Relationship ◽  
Correlated Noises

We studied the effect of additive and multiplicative noises on the growth of a tumor based on a logistic growth model. The steady-state probability distribution and the average population of the tumor cells were given to explain the important roles of correlated noises in the tumor growth. We explored that multiplicative noise induces a phase transition of the tumor growth from a uni-stable state to a bi-stable state; the relationship between the intensity of multiplicative noise and the population of the tumor cells shows a stochastic resonance-like characteristic. It was also confirmed that additive noise weakened rather than extinguish the tumor growth. Homologous noises, however, promote the growth of a tumor. We also discussed about the relationship between the tumor treatment and the model.

scholarly journals Steady state of overdamped particles in the non-conservative force field of a simple non-linear model of optical trap

2021 ◽  
Vol 2021 (11) ◽  
pp. 113205
Author(s):  
Matthieu Mangeat ◽  
Thomas Guérin ◽  
David S Dean
Keyword(s):  
Steady State ◽  
Force Field ◽  
Brownian Particle ◽  
Optical Trap ◽  
Three Dimensional ◽  
Planck Equation ◽  
Steady State Probability ◽  
Trapped Particles ◽  
Scattering Force ◽  
Optically Trapped

Abstract Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper, we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to a commonly used force field model for an optical trap. The model is the simplest of its kind that takes into account non-conservative forces. In particular, we present the exact results for certain marginals of the full three-dimensional steady state probability distribution, in addition to results for the toroidal probability currents that are present in the steady state, as well as for the circulation of these currents. Our analytical results are confirmed by numerical solution of the steady state Fokker–Planck equation.

scholarly journals Multipreconditioned GMRES for simulating stochastic automata networks

2018 ◽  
Vol 16 (1) ◽  
pp. 986-998
Author(s):  
Chun Wen ◽  
Ting-Zhu Huang ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen ◽  
Hong-Fan Zhang ◽  
...  
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Linear Systems ◽  
Iterative Methods ◽  
Communication Systems ◽  
Queueing Systems ◽  
Steady State Probability ◽  
Stochastic Automata ◽  
Automata Networks ◽  
Generator Matrices

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

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