Effects of multiplicative colored noise on bacteria growth

Liao, Hongyan; Ai, Bao-quan; Hu, Lian

doi:10.1590/s0103-97332007000700009

Cited by 15 publications

(7 citation statements)

References 9 publications

(11 reference statements)

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“…We show that for fixed parameter values the stationary PDFs are always gamma distributions (e.g. [36,37]), one of the most popular distributions used in fitting experimental data. However, we find numerically that the time-dependent PDFs in transitioning from one set of parameter values to another are significantly different from gamma distributions, especially for strong stochastic noise.…”

Section: Introductionmentioning

confidence: 94%

Far-From-Equilibrium Time Evolution between Two Gamma Distributions

Kim

Tenkès

Hollerbach

et al. 2017

Entropy

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Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time-dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem and show that as the strength of the stochastic noise increases, the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise, a transition occurs whereby the PDF never reaches a stationary state, but instead, forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analysed in terms of entropy and information length, the total number of statistically-distinguishable states that a system passes through in time.

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Section: Introductionmentioning

confidence: 94%

Far-From-Equilibrium Time Evolution between Two Gamma Distributions

Kim

Tenkès

Hollerbach

et al. 2017

Entropy

View full text Add to dashboard Cite

show abstract

“…We show that for fixed parameter values the stationary PDFs are always gamma distributions (e.g. [32,33]), one of the most popular distributions used in fitting experimental data. However, we find numerically that the time-dependent PDFs in transitioning from one set of parameter values to another are significantly different from gamma distributions, especially for strong stochastic noise.…”

Section: Introductionmentioning

confidence: 94%

Far-from-Equilibrium Time Evolution between two Gamma Distributions

Kim¹,

Tenkès²,

Hollerbach³

2017

Preprint

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Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially timedependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions.For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

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“…While some therapies, such as chemotherapy, surgery, and radiotherapy, are usually described by multiplicative noise [23] . Thus, there has been great much research on the effect of additive noise or multiplicative noise on tumor growth system [24] , [25] , [26] , [27] , [28] , [29] . Ref.…”

Section: Introductionmentioning

confidence: 99%