Analysis of nonlinear stochastic oscillations in the biochemical Goldbeter model

Bashkirtseva, Irina; Ryashko, Lev; Zaitseva, Svetlana

doi:10.1016/j.cnsns.2019.02.008

Cited by 19 publications

(5 citation statements)

References 17 publications

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“…In the interval ν 2 < ν 1, the system again has only stable equilibria. Note that near the bifurcation points ν 1 , ν 2 , because of strong nonlinearity, a phenomenon of Canard explosion is observed [26].…”

Section: Noise-induced Phenomena In Goldbeter Modelmentioning

confidence: 98%

“…First, for ε = 0.1, the system (2) exhibits a phenomenon of stochastic excitement: trajectories starting from the stable equilibrium show an alternation of small-amplitude oscillations near the equilibrium and large-amplitude spike-type stochastic outbreaks (see phase trajectories and time series in figure 2(a) shown in red). The probabilistic mechanism of such noise-induced excitement was studied in detail in [26].…”

Section: Noise-induced Phenomena In Goldbeter Modelmentioning

confidence: 99%

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How additive noise forms and shifts phantom attractors in slow–fast systems

Bashkirtseva¹,

Ryashko²

2020

J. Phys. A: Math. Theor.

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We present a peculiar phenomenon of the formation and shift of a localized random distribution in slow-fast systems forced by additive white Gaussian noise. Location of such 'phantom' attractors in zones far from deterministic attractors is theoretically analysed by the method of freezing and averaging. This method is applied to the analysis of the Goldbeter enzymatic model and FitzHugh-Nagumo neural model, in which noise-induced formation and shifts of 'phantom' attractors are detected.

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Section: Noise-induced Phenomena In Goldbeter Modelmentioning

confidence: 98%

Section: Noise-induced Phenomena In Goldbeter Modelmentioning

confidence: 99%

How additive noise forms and shifts phantom attractors in slow–fast systems

Bashkirtseva¹,

Ryashko²

2020

J. Phys. A: Math. Theor.

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“…One of the approaches for the construction of such approximations is based on the stochastic sensitivity function technique [25][26][27]. This technique was successfully used in the analysis of the stochastic excitability in neuronal dynamics [28,29], chemical kinetics [30] and population dynamics [31].…”

Section: Introductionmentioning

confidence: 99%

Constructive role of noise and diffusion in an excitable slow–fast population system

Bashkirtseva

Панкратов

Slepukhina

et al. 2020

Phil. Trans. R. Soc. A.

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We study the effects of noise and diffusion in an excitable slow–fast population system of the Leslie–Gower type. The phenomenon of noise-induced excitement is investigated in the zone of stable equilibria near the Andronov–Hopf bifurcation with the Canard explosion. The stochastic generation of mixed-mode oscillations is studied by numerical simulation and stochastic sensitivity analysis. Effects of the diffusion are considered for the spatially distributed variant of this slow–fast population model. The phenomenon of the diffusion-induced generation of spatial patterns-attractors in the Turing instability zone is demonstrated. The multistability and variety of transient processes of the pattern formation are discussed. This article is part of the theme issue ‘Patterns in soft and biological matters’.

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“…[3][4][5][6][7] Here, one can mention noise-induced transitions, 8,9 stochastic excitability, 10 noise-induced transition from order to chaos, 11,12 stochastic and coherence resonance, 13 and so on. These phenomena are observed in physics, [14][15][16] chemistry, 5,17,18 and biology. [19][20][21] The development of mathematical methods for the analysis of noise-induced phase transitions is one of the urgent problems of modern nonlinear science.…”

Section: Introductionmentioning

confidence: 99%

Stochastic sensitivity analysis of mixed‐mode oscillations in kinetics of the flow reactor

Bashkirtseva

2020

Math Methods in App Sciences

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In this paper, phase transitions associated with transformations of oscillation regimes in stochastic thermochemical systems are studied. A system of two differential equations specifying the dynamics of the reactant and temperature is used as a conceptual model. On the basis of this model, we investigate how random disturbances can deform equilibrium and periodic regimes of unforced deterministic system and form new complex mixed-mode oscillations. Along with the results extracted from the direct numerical simulation, a new theoretical approach to the analysis of these fluctuation phenomena using the stochastic sensitivity function technique and confidence domains is demonstrated.

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Analysis of nonlinear stochastic oscillations in the biochemical Goldbeter model

Cited by 19 publications

References 17 publications

How additive noise forms and shifts phantom attractors in slow–fast systems

How additive noise forms and shifts phantom attractors in slow–fast systems

Constructive role of noise and diffusion in an excitable slow–fast population system

Stochastic sensitivity analysis of mixed‐mode oscillations in kinetics of the flow reactor

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