Phase Diagrams of Noise Induced Transitions: Exact Results for a Class of External Coloured Noise

Kitahara, Kakuo; Horsthemke, Werner; Lefever, René; Inaba, Yutaka

doi:10.1143/ptp.64.1233

Cited by 113 publications

(34 citation statements)

References 7 publications

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“…If we consider the case which only has one telegraph then our result is exactly the same as what has been obtained by Kitahara et al [13] and has been used in our previous paper [10]. The case of two telegraphs is a subject of our analysis in the next sections.…”

Section: The Equation For the Stationary Probability Distributionsupporting

confidence: 79%

An Exactly Soluble Equation for the Stationary Probability Distribution in a Nonlinear System under the Influence of Two-telegraph Noise: Application to the Noise Reduction in a Raman Ring Laser

Khoa¹,

Lanh²,

Sanh³

et al. 2016

Comm. in Phys.

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Abstract. In this paper, we will consider a nonlinear system with random telegraph noises in a Raman ring laser by modeling the laser pump light as a pre-Gaussian process and find an exactly soluble equation for the stationary probability distribution of fluctuations in this nonlinear system under the influence of two-telegraph noise. As a consequence, we will obtain the so-called noise reduction in this system: the Stokes output of this laser tends to stabilize under the influence of the broad-band two-telegraph pre-Gaussian pump and compare this result with that obtained in our previous paper (Cao Long Van, Doan Quoc Khoa, Opt. Quant. Electron. 43 (2012) 137) for the case of one-telegraph noise.

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Section: The Equation For the Stationary Probability Distributionsupporting

confidence: 79%

An Exactly Soluble Equation for the Stationary Probability Distribution in a Nonlinear System under the Influence of Two-telegraph Noise: Application to the Noise Reduction in a Raman Ring Laser

Khoa¹,

Lanh²,

Sanh³

et al. 2016

Comm. in Phys.

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“…First, the corresponding Fokker-Planck equation is written for Equation (4), then, using the Fokker-Planck equation, the equations for moments are derived. Since the basic equation is the phenomenological Equation (2), in which the fluctuating parameter c f (t) has been approximated by the Gaussian white noise, then according to Horsthemke and Lefever (1984), the most appropriate diffusion process is the process which follows from the Stratonovich interpretation of the SDE and the corresponding Fokker-Planck equation for SDE (4), as shown in Kitahara et al (1980), will have the form…”

Section: Theorymentioning

confidence: 99%

“…The effect of the action of the external noise essentially depends on the type of the noise, whether it is Langevene or multiplicative. As a rule, the action of the Langevene noise does not lead to qualitative changes in the behavior of a deterministic system while under the action of a multiplicative noise, a qualitative change in the system behavior is to be expected (De la Rubia & Velarde, 1978;Kitahara, Horsthemke, Lefever, & Inaba, 1980). In paper Arakelyan, Haroutiunian, Arakelyan, and Haroutiunian (2002), the action of the Langevene noise on ligand adsorption on DNA has been investigated.…”

Section: Introductionmentioning

confidence: 99%

Isotherm of ligand adsorption on DNA at multiplicative noise

Arakelyan

Harutyunyan

Andriasyan

et al. 2012

Journal of Biomolecular Structure and Dynamics

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Fluctuations of the number of ligands adsorbed on macromolecules are considered in the case when the number of ligands in the solution fluctuates under the action of fluctuations of the external medium (external noise). For the case of small filling, the multiplicative type of stochastic differential equation is obtained, describing the time variation of the number of ligands adsorbed on macromolecules. The isotherm of adsorption of ligands on DNA is obtained. It is shown that at small ligand concentrations, for some relations between adsorption parameters and the intensity of the external noise, no macromolecule adsorption of ligands takes place.

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“…Generally, the finite correlation of the noise will have an effect on the form of the stationary probability. This fact has been exploited in recent studies of so-called colored noise induced transitions [13][14][15][16][17][18]. Because the underlying dynamics are governed by a non-Markovian process, the exact master equation can be obtained in special cases only [5, 12-14, 18, 19].…”

Section: Introductionmentioning

confidence: 99%

Bistable flow driven by coloured gaussian noise: A critical study

Hänggi

Marchesoni

Grigolini

1984

Z. Physik B - Condensed Matter

206

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A one-dimensional bistable flow driven by additive, exponentially correlated Gaussian noise is considered. The small relaxation time Fokker-Planck approximations, widely used in the recent literature, are derived and possible shortcomings of those approximation schemes are discussed. In particular, it is pointed out that higher order nonFokker-Planck type contributions are generally of the same order as the Fokker-Planck terms. In principle, those contributions cannot be neglected if the global behavior of the probability solutions is to be described accurately. The result for the activation rate (Arrhenius factor), as evaluated from the approximative Fokker-Planck schemes, does not coincide in leading order in the correlation time z of the noise with a computer simulation of the rate at low noise level. This result indicates that the wings of the stationary probability /~(x) are in leading order in ~ not recovered correctly from the approximative Fokker-Planck schemes. Some implications of our study for adiabatic elimination procedures are also discussed.

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Phase Diagrams of Noise Induced Transitions: Exact Results for a Class of External Coloured Noise

Cited by 113 publications

References 7 publications

An Exactly Soluble Equation for the Stationary Probability Distribution in a Nonlinear System under the Influence of Two-telegraph Noise: Application to the Noise Reduction in a Raman Ring Laser

An Exactly Soluble Equation for the Stationary Probability Distribution in a Nonlinear System under the Influence of Two-telegraph Noise: Application to the Noise Reduction in a Raman Ring Laser

Isotherm of ligand adsorption on DNA at multiplicative noise

Bistable flow driven by coloured gaussian noise: A critical study

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