Stochastic bifurcation analysis in Brusselator system with white noise

Li, Changzhao; Zhang, Juan

doi:10.1186/s13662-019-2287-x

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…S2G). This well-known phenomenon is called a stochastic Hopf bifurcation (Schenk-Hoppé, 1996; Ma, 2012; Arnold et al, 1999; Li and Zhang, 2019; Simpson et al, 2021). The noise-induced oscillations have a frequency whose value is related to the imaginary part of the eigenvalues of the Jacobian at the fixed point underlying deterministic dynamics.…”

Section: Resultsmentioning

confidence: 99%

Gene expression noise accelerates the evolution of a biological oscillator

Lin

Buchler

2022

Preprint

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Gene expression is a biochemical process, where stochastic binding and un-binding events naturally generate fluctuations and cell-to-cell variability in gene dynamics. These fluctuations typically have destructive consequences for proper biological dynamics and function (e.g., loss of timing and synchrony in biological oscillators). Here, we show that gene expression noise counter-intuitively accelerates the evolution of a biological oscillator and, thus, can impart a benefit to living organisms. We used computer simulations to evolve two mechanistic models of a biological oscillator at different levels of gene expression noise. We first show that gene expression noise induces oscillatory-like dynamics in regions of parameter space that cannot oscillate in the absence of noise. We then demonstrate that these noise-induced oscillations generate a fitness landscape whose gradient robustly and quickly guides evolution by mutation towards robust and self-sustaining oscillation. These results suggest that noise can help dynamical systems evolve or learn new behavior by revealing cryptic dynamic phenotypes outside the bifurcation point.

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Section: Resultsmentioning

confidence: 99%

Gene expression noise accelerates the evolution of a biological oscillator

Lin

Buchler

2022

Preprint

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“…Li and Wang [7] have explored the hopf bifurcation and diffusion-driven instability of a Brusselator system. Li and Zhang [8] have studied stochastic bifurcation and stability of a continuous Brusselator system with multiplicative white noise. More precisely, Li and Zhang [8] have transformed the original continuous Brusselator system to an Itô averaging system by polar coordinates transformation and the stochastic averaging method.…”

Section: Review Of Literature and Statement Of The Problemmentioning

confidence: 99%

“…Li and Zhang [8] have studied stochastic bifurcation and stability of a continuous Brusselator system with multiplicative white noise. More precisely, Li and Zhang [8] have transformed the original continuous Brusselator system to an Itô averaging system by polar coordinates transformation and the stochastic averaging method. Furthermore, the local and global stabilities are analyzed by the singular boundary theory and largest Lyapunov exponent, and phenomenological bifurcation is also studies by examining the associated Fokker-Planck equation.…”

Section: Review Of Literature and Statement Of The Problemmentioning

confidence: 99%

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

2022

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The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point P 1 , r if r > 0 . Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point P 1 , r . Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if r , h ∈ ℋℬ | P 1 , r = r , h , h = 2 − r and r , h ∈ ℱℬ | P 1 , r = r , h , h = 4 / 2 − r − r 2 − 4 r , respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically.

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