The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

Du, Lingling; Mei, Dong-Cheng

doi:10.1016/j.physleta.2010.06.003

Cited by 27 publications

(7 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, the larger the damping coefficient, the larger the amplitude of the high‐frequency signal required to achieve the optimized response amplitude. In a word, the vibration resonance curve reenters from unimodal structure to bimodal structure and then to unimodal structure again with the increase of damping coefficient, that is, a reentrance phenomenon [34, 35].…”

Section: Resultsmentioning

confidence: 99%

An analog circuit experiment on vibrational resonance of an underdamped bistable system

Liu

Jiang

et al. 2022

The Journal of Engineering

View full text Add to dashboard Cite

The underdamped vibrational resonance of a bistable analogue circuit is investigated. For a wide range of damping coefficients, vibrational resonance phenomena are more robust than over-damped states. In particular, the vibration resonance curve reenters from single peak to double peak and then to single peak again with the increase of damping coefficients, that is, a reentrance phenomenon. The experimental results are consistent with the theoretical ones. The experiment constructed a framework for amplifying weak signals within underdamped regimes.

show abstract

Section: Resultsmentioning

confidence: 99%

An analog circuit experiment on vibrational resonance of an underdamped bistable system

Liu

Jiang

et al. 2022

The Journal of Engineering

View full text Add to dashboard Cite

show abstract

“…The degradation rate is regarded to be proportional to their concentration or copy number. However, due to the limited carrying capacity of the environment for degradation, such as the limited catabolic enzymes and ATP, the degradation rate should be restrained and thus it deviates from this linear relationship in particular when the concentration or copy numbers of the RNA or proteins are large, which is analogous to the logistic model for tumor cell growth [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Effects of restrained degradation on gene expression and regulation

et al. 2020

View full text Add to dashboard Cite

The effects of carrying capacity of environment K for degradation (the K effect for short) on the constitutive gene expression and a simple genetic regulation system, are investigated by employing a stochastic Langevin equation combined with the corresponding Fokker-Planck equation for the two stochastic systems subjected to internal and external noises. This K effect characterizes the limited degradation ability of the environment for RNA or proteins, such as insufficient catabolic enzymes. The K effect could significantly change the distribution of mRNA copy-number in constitutive gene expression, and interestingly, it leads to the Fano factor slightly larger than 1 if only the internal noise exists. Therefore, that the recent experimental measurements suggests the Fano factor deviates from 1 slightly (Science 346 (2014) 1533), probably originates from the K effect. The K effects on the steady and transient properties of genetic regulation system, have been investigated in detail.It could enhance the mean first passage time significantly especially when the noises are weak and reduce the signal-to-noise ratio in stochastic resonance substantially.

show abstract

“…Well-known examples include biophysiological controls [41], neuronal networks [42] , and optical cavities [43,44]. At the same time, it appears that the combination of time delay and noise is ubiquitous in nature and often changes fundamentally the dynamics of the system [45][46][47][48][49]. From the discussion above, a significant and intriguing question naturally arises: what will happen if time delay and noises are simultaneously considered in a tumor growth model under immune surveillance, when periodic signals are introduced both multiplicatively and additively?…”

Section: Introductionmentioning

confidence: 99%

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

et al. 2014

View full text Add to dashboard Cite

Abstract:The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance. PACS

show abstract

The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

Cited by 27 publications

References 26 publications

An analog circuit experiment on vibrational resonance of an underdamped bistable system

An analog circuit experiment on vibrational resonance of an underdamped bistable system

Effects of restrained degradation on gene expression and regulation

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

Contact Info

Product

Resources

About