Noise-induced phantom attractor in the enzyme kinetics

Bashkirtseva, Irina; Zaitseva, Svetlana; Pisarchik, Alexander N.

doi:10.1063/1.5130805

Cited by 2 publications

(1 citation statement)

References 8 publications

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“…These phenomena can be interpreted as the stochastic generation of birhytmicity in the system that is monostable in the deterministic case. An increasing noise in this model can result in the new phenomenon of the 'phantom attractor' that means the shift and localization of random states far from the deterministic attractors [51].…”

Section: Introductionmentioning

confidence: 99%

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Bashkirtseva¹,

Ryashko²,

Zaitseva

2020

J. Phys. A: Math. Theor.

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A mathematical model of the biochemical reaction with nonlinear recycling of the product into substrate is considered. The main control parameter of this model is the substrate injection rate, which is subject to random disturbances. We study noise-induced oscillations in the parameter zones where the system is bistable and exhibit a coexistence of the equilibrium and limit cycle, or two stable cycles (birhythmicity). Phenomena of the generation of noisy birhythmicity and 'stochastic preference' of attractors are studied on the basis of the stochastic sensitivity function technique, confidence domains method, and statistics of interspike intervals.

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Section: Introductionmentioning

confidence: 99%

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Bashkirtseva¹,

Ryashko²,

Zaitseva

2020

J. Phys. A: Math. Theor.

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Stochastic Bifurcations, Chaos and Phantom Attractors in the Langford System with Tori

Bashkirtseva

Ryashko

2020

Int. J. Bifurcation Chaos

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The variability of stochastic dynamics for a three-dimensional dynamic model in a parametric zone with 2-tori is investigated. It is shown how weak Gaussian noise transforms deterministic quasiperiodic oscillations into noisy bursting. The phenomenon of stochastic generation of a phantom attractor and its shift with noise amplification is revealed. This phenomenon, accompanied by order-chaos transitions, is studied in terms of stochastic [Formula: see text]- and [Formula: see text]-bifurcations.

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Noise-induced phantom attractor in the enzyme kinetics

Cited by 2 publications

References 8 publications

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Stochastic sensitivity analysis of noise-induced transitions in a biochemical model with birhythmicity

Stochastic Bifurcations, Chaos and Phantom Attractors in the Langford System with Tori

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