A Novel Stochastic Bifurcation and its Discrimination

2021 ◽  
Author(s):  
Chen Jin ◽  
Zhongkui Sun ◽  
Wei Xu
Keyword(s):  
Stochastic Bifurcation

Feedback-Induced Variations of Distribution in a Representative Gene Model

2015 ◽  
Vol 25 (07) ◽  
pp. 1540008
Author(s):  
Peijiang Liu ◽  
Zhanjiang Yuan ◽  
Lifang Huang ◽  
Tianshou Zhou
Keyword(s):  
Gene Expression ◽  
Power Law ◽  
Positive Feedback ◽  
Bimodal Distribution ◽  
Stochastic Bifurcation ◽  
Protein Distribution ◽  
Identical Cell ◽  
Induced Changes ◽  
Gene Switching ◽  
Cell To Cell Variability

Gene expression is inherently noisy, implying that the number of mRNAs or proteins is not invariant rather than follows a distribution. This distribution can not only provide the exact information on the dynamics of gene expression but also describe cell-to-cell variability in a genetically identical cell population. Here, we systematically investigate a two-state model of gene expression, a model paradigm used to study expression dynamics, focusing on the effect of feedback on the type of mRNA or protein distribution. If there is no feedback, then the distribution may be bimodal, power-law tailed, or Poisson-like, depending on gene switching rates. However, we find that feedback can tune or change the type of the distribution in each case and tends to unimodalize the distribution as its strength increases. Specifically, positive feedback can change not only a power-law tailed distribution into a bimodal or Poisson-like distribution but also a bimodal distribution into a Poisson-like distribution (implying that stochastic bifurcation can take place). In addition, it can make a Poisson-like distribution become more peaked but does not change the type of this distribution. In contrast to positive feedback, negative feedback has less influence on the shape of the distributions except for the bimodal case. In all cases, the noise-feedback curve used extensively in previous studies cannot well reflect the feedback-induced changes in the shape of distributions. Feedback-induced variations in distribution would be important for cell survival in fluctuating environments.

Structural Modal Multifurcation With Internal Resonance: Part 2—Stochastic Approach

1993 ◽  
Vol 115 (2) ◽  
pp. 193-201 ◽  
Author(s):  
R. A. Ibrahim ◽  
B. H. Lee ◽  
A. A. Afaneh
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Axial Load ◽  
Random Excitation ◽  
Stochastic Bifurcation ◽  
Density Level ◽  
Analytical Treatment ◽  
Asymmetric Mode ◽  
Non Gaussian ◽  
Gaussian Closure

Stochastic bifurcation in moments of a clamped-clamped beam response to a wide band random excitation is investigated analytically, numerically, and experimentally. The nonlinear response is represented by the first three normal modes. The response statistics are examined in the neighborhood of a critical static axial load where the normal mode frequencies are commensurable. The analytical treatment includes Gaussian and non-Gaussian closures. The Gaussian closure fails to predict bifurcation of asymmetric modes. Both non-Gaussian closure and numerical simulation yield bifurcation boundaries in terms of the axial load, excitation spectral density level, and damping ratios. The results of both methods are in good agreement only for symmetric response characteristics. In the neighborhood of the critical bifurcation parameter the Monte Carlo simulation yields strong nonstationary mean square response for the asymmetric mode which is not directly excited. Experimental and Monte Carlo simulation exhibit nonlinear features including a shift of the resonance peak in the response spectra as the excitation level increases. The observed shift is associated with a widening effect in the response bandwidth.

Theory of stochastic bifurcation in BWRs and applications

2003 ◽  
Vol 43 (1-4) ◽  
pp. 201-207 ◽  
Author(s):  
H. Konno ◽  
S. Kanemoto ◽  
Y. Takeuchi
Keyword(s):  
Stochastic Bifurcation

scholarly journals Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Julien Hurbain ◽  
Darka Labavić ◽  
Quentin Thommen ◽  
Benjamin Pfeuty
Keyword(s):  
Cell Fate ◽  
Stochastic Dynamics ◽  
Biochemical Networks ◽  
Stochastic Bifurcation ◽  
Modeling Framework ◽  
Life And Death ◽  
Cell Fate Decisions ◽  
Wide Range ◽  
Adaptation Response ◽  
The Impact

Abstract Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Stochastic Bifurcation Processes and Distributions of Fractions

1993 ◽  
Vol 88 (421) ◽  
pp. 345-354
Author(s):  
Roman Krzysztofowicz ◽  
Sharon Reese
Keyword(s):  
Stochastic Bifurcation

Bifurcation Analysis of a Vibro-Impact Viscoelastic Oscillator with Fractional Derivative Element

2018 ◽  
Vol 28 (14) ◽  
pp. 1850170 ◽  
Author(s):  
Yong-Ge Yang ◽  
Wei Xu ◽  
YangQuan Chen ◽  
Bingchang Zhou
Keyword(s):  
Fractional Derivative ◽  
Numerical Solutions ◽  
Gaussian White Noise ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Stochastic Bifurcation ◽  
Damping Force ◽  
Impact Oscillator ◽  
Viscoelastic Parameters ◽  
Viscoelastic Term

To the best of authors’ knowledge, little work has been focused on the noisy vibro-impact systems with fractional derivative element. In this paper, stochastic bifurcation of a vibro-impact oscillator with fractional derivative element and a viscoelastic term under Gaussian white noise excitation is investigated. First, the viscoelastic force is approximately replaced by damping force and stiffness force. Thus the original oscillator is converted to an equivalent oscillator without a viscoelastic term. Second, the nonsmooth transformation is introduced to remove the discontinuity of the vibro-impact oscillator. Third, the stochastic averaging method is utilized to obtain analytical solutions of which the effectiveness can be verified by numerical solutions. We also find that the viscoelastic parameters, fractional coefficient and fractional derivative order can induce stochastic bifurcation.

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