Noise-Induced Hypersensitivity to Small Time-Dependent Signals

Ginzburg, S. L.; Pustovoit, M. A.

doi:10.1103/physrevlett.80.4840

Cited by 28 publications

(20 citation statements)

References 9 publications

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“…the system exhibits supersensitivity to extremely weak modulation close to the critical point. This sensitivity was also reported in an overdamped Kramers oscillator with multiplicative noise free from additive noise (σ 2 = 0), which is a specific example in this class of systems [12]. In the absence of s(t), the system produces symmetric bursting pattern with x(t) = 0; while the bursting pattern is reorganized to manifest the weak signal after it is fed into the system (see Fig.…”

Section: Robustness Of Supersensitivity To the Weak Signalsupporting

confidence: 58%

Symmetry-breaking on-off intermittency under modulation: Robustness of supersensitivity, resonance, and information gain

Zhou

2000

Phys. Rev. E

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Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of symmetric systems, the intermittency is symmetry-breaking [Ying-Cheng Lai, Phys. Rev. E 53. R4267 (1996)]. We report interesting and practically important universal behavior of robustness of supersensitivity, resonance and information gain in this class of systems when subjected to a weak modulation. While intermittent loss of synchronization may be harmful to application of high-quality synchronization of coupled chaotic systems, the features reported here may lead to interesting application of on-off intermittency. PACS number(s): 05.40.-a, 05.45.-a

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Section: Robustness Of Supersensitivity To the Weak Signalsupporting

confidence: 58%

Symmetry-breaking on-off intermittency under modulation: Robustness of supersensitivity, resonance, and information gain

Zhou

2000

Phys. Rev. E

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“…This phenomenon was discovered rather recently, and a lot of attention was given to several of its variants, both theoretically, see Refs. [69,70,71,72,73,74,75,76], and experimentally, see Refs. [77,78,79,80,81].…”

Section: Nonlinear and Hypersensitive Response With Dmnmentioning

confidence: 98%

Dichotomous Markov Noise: Exact Results for Out-of-Equilibrium Systems

Bena

2006

Int. J. Mod. Phys. B

136

144

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Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications -the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on a par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.

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“…21 Dichotomous noise generally breaks detailed balance in the circuits and thus creates non-equilibrium steady states which cannot always be described by quasi-equilibrium fluctuation statistics. Dichotomous noise driven phenomena include robust phase synchronization, 22,23 stochastic hypersensitivity, 24,25 enhanced stochastic resonance, 26 hysteresis, 27 and patterning. 28,29 Brute force simulation of the full master equation for genetic networks has already yielded many insights.…”

Section: Introductionmentioning

confidence: 99%

Dichotomous noise models of gene switches

Potoyan

Wolynes

2015

The Journal of Chemical Physics

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Molecular noise in gene regulatory networks has two intrinsic components, one part being due to fluctuations caused by the birth and death of protein or mRNA molecules which are often present in small numbers and the other part arising from gene state switching, a single molecule event. Stochastic dynamics of gene regulatory circuits appears to be largely responsible for bifurcations into a set of multi-attractor states that encode different cell phenotypes. The interplay of dichotomous single molecule gene noise with the nonlinear architecture of genetic networks generates rich and complex phenomena. In this paper, we elaborate on an approximate framework that leads to simple hybrid multi-scale schemes well suited for the quantitative exploration of the steady state properties of large-scale cellular genetic circuits. Through a path sum based analysis of trajectory statistics, we elucidate the connection of these hybrid schemes to the underlying master equation and provide a rigorous justification for using dichotomous noise based models to study genetic networks. Numerical simulations of circuit models reveal that the contribution of the genetic noise of single molecule origin to the total noise is significant for a wide range of kinetic regimes. C 2015 AIP Publishing LLC. [http://dx

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Noise-Induced Hypersensitivity to Small Time-Dependent Signals

Abstract: For a simple example of on-off intermittency, an overdamped Kramers oscillator with multiplicative noise, we demonstrate a phenomenon of hypersensitivity to ultrasmall time-dependent signals.[S0031-9007(98)06229-2] PACS numbers: 05.40.+j, 05.45.+b

Cited by 28 publications

References 9 publications

Symmetry-breaking on-off intermittency under modulation: Robustness of supersensitivity, resonance, and information gain

Symmetry-breaking on-off intermittency under modulation: Robustness of supersensitivity, resonance, and information gain

Dichotomous Markov Noise: Exact Results for Out-of-Equilibrium Systems

Dichotomous noise models of gene switches

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