Noise Induced Bistability of Parametric Surface Waves

Residori, Stefania; Berthet, R.; Roman, Benoît; Fauve, S.

doi:10.1103/physrevlett.88.024502

Cited by 29 publications

(28 citation statements)

References 19 publications

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“…While there are observations of noise-induced bistabilities in other physical and engineering systems (27,28), there is little such conclusive experimental evidence in biomolecular structures to date, although it might be difficult to deconvolve the hereinpredicted effects from the measurement noise. Furthermore, single-cell measurements of protein activity and gene expression are (although increasing) few, and of those, fewer still follow single-cell expression temporally at sufficient resolution.…”

Section: Discussionmentioning

confidence: 99%

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

Samoilov

Plyasunov²,

Arkin³

2005

Proc. Natl. Acad. Sci. U.S.A.

325

332

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Stochastic effects in biomolecular systems have now been recognized as a major physiologically and evolutionarily important factor in the development and function of many living organisms. Nevertheless, they are often thought of as providing only moderate refinements to the behaviors otherwise predicted by the classical deterministic system description. In this work we show by using both analytical and numerical investigation that at least in one ubiquitous class of (bio)chemical-reaction mechanisms, enzymatic futile cycles, the external noise may induce a bistable oscillatory (dynamic switching) behavior that is both quantitatively and qualitatively different from what is predicted or possible deterministically. We further demonstrate that the noise required to produce these distinct properties can itself be caused by a set of auxiliary chemical reactions, making it feasible for biological systems of sufficient complexity to generate such behavior internally. This new stochastic dynamics then serves to confer additional functional modalities on the enzymatic futile cycle mechanism that include stochastic amplification and signaling, the characteristics of which could be controlled by both the type and parameters of the driving noise. Hence, such noise-induced phenomena may, among other roles, potentially offer a novel type of control mechanism in pathways that contain these cycles and the like units. In particular, observations of endogenous or externally driven noiseinduced dynamics in regulatory networks may thus provide additional insight into their topology, structure, and kinetics.network motif ͉ signal transduction ͉ chemical reaction ͉ synthetic biology ͉ systems biology

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Section: Discussionmentioning

confidence: 99%

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

Samoilov

Plyasunov²,

Arkin³

2005

Proc. Natl. Acad. Sci. U.S.A.

325

332

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“…In order to destroy the narrow band time response of the waves, we have repeated our experiments using parametric excitation with Gaussian noise in the frequency band f 0 ͓30, 50͔ Hz. Noise driven parametric surface waves have been studied by Residori et al 27 In our case, noise gives rise to an intermittent temporal global surface response: the surface randomly alternates between episodes with turbulent waves and the flat state. We have found that with parametric excitation by noise, only the first three peaks in the frequency spectrum are discernible, but all our conclusions regarding the spectral exponents remained unaltered.…”

Section: -5mentioning

confidence: 99%

Turbulent parametric surface waves

2009

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We study disordered capillary waves on the surface of a vertically oscillated fluid layer and try to establish their relation with weak wave turbulence. We measure the surface gradient in space and time and argue that gradient spectra are better suited for comparison to the predictions of weak wave turbulence theory than spectra of the surface elevation. Because the gradient is a vector quantity, we must distinguish longitudinal and transverse spectra. However, they prove to be related trivially through isotropy. From the measured wavenumber-frequency spectrum it appears that the dispersion relation is only satisfied approximately. In the wavenumber direction the spectral features are strongly broadened due to spatial disorder. This disagrees with weak wave turbulence theory where exact satisfaction of the dispersion relation is pivotal. We find approximate algebraic frequency and wavenumber spectra but with exponents that are different from those predicted by weak wave turbulence theory. However, other findings, such as the broadening of harmonics proportional to their frequency and the emergence of Gaussian statistics at selected wavenumber bands, point to weak wave turbulence.

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“…Only recently, experiments on the effect of noise on parametrically driven surface waves have been performed in the case of a subcritical bifurcation. New phenomena, such as noise-induced-bistability, have been reported [11].…”

Section: Introductionmentioning

confidence: 99%

Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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We report a study on the effect of external multiplicative noise on parametric instabilities using two different experimental systems: an electronic RLC circuit, parametrically pumped with a voltage-variable capacitor, and surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). Both systems are forced by the superposition of a sinusoidal and a noisy component. We study the statistical properties of the response of both systems to noisy parametric forcing and compare them with theoretical predictions. When the detuning from parametric resonance is such that the bifurcation in the absence of noise is supercritical, both systems behave in the same way under the influence of noise. We find that the effect of noise is twofold: on one hand, it triggers the instability before its deterministic onset under the form of oscillatory bursts; on the other hand, it inhibits the nonlinearly saturated oscillatory response above the deterministic onset. When the detuning is such that the bifurcation is subcritical, we find that the two systems behave differently. In the case of the electronic oscillator, noise mostly triggers random transitions between the two states of the bistable region that exists in the absence of noise, whereas in the surface wave experiment new states are created by noise and the bistable region is strongly enlarged.

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Noise Induced Bistability of Parametric Surface Waves

Cited by 29 publications

References 19 publications

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

Turbulent parametric surface waves

Effect of multiplicative noise on parametric instabilities

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