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Influence of random fluctuations on delayed bifurcations: the case of additive white noise

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Influence of random fluctuations on delayed bifurcations : the case of additive white noise. / Stocks, N. G.; Mannella, R.; McClintock, Peter V. E.

In: Physical review a, Vol. 40, No. 9, 01.11.1989, p. 5361-5369.

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Stocks, N. G. ; Mannella, R. ; McClintock, Peter V. E. / Influence of random fluctuations on delayed bifurcations : the case of additive white noise. In: Physical review a. 1989 ; Vol. 40, No. 9. pp. 5361-5369.

Bibtex

@article{bc89918733f34e68b9692111418e9e7e,
title = "Influence of random fluctuations on delayed bifurcations: the case of additive white noise",
abstract = "The influence of additive white noise on the delay of a bifurcation point in the presence of a swept control parameter has been studied by analog experiment and digital simulation. Measurements of the time taken for the second moment [x^2(t)] to reach a given threshold are in excellent agreement with the calculations of Zeghlache, Mandel, and Van den Broeck [Phys, Rev. A 40, 286 (1989)). It is demonstrated, however, that the mean first-passage time (MFPT) for x^2(t) to attain the same threshold, corresponding to the quantity that is usually determined in laser experiments, can be markedly different. It may be either larger or smaller, depending on the conditions under which the measurements are made. A calculation of the MFPT is presented and shown to be in excellent agreement with the experimental measurements and to reduce, in the relevant limit, to the theoretical results previously published by Torrent and San Miguel [Phys. Rev. A 38, 245 (1988)].",
author = "Stocks, {N. G.} and R. Mannella and McClintock, {Peter V. E.}",
year = "1989",
month = nov,
day = "1",
doi = "10.1103/PhysRevA.40.5361",
language = "English",
volume = "40",
pages = "5361--5369",
journal = "Physical review a",
issn = "1050-2947",
publisher = "American Physical Society",
number = "9",

}

RIS

TY - JOUR

T1 - Influence of random fluctuations on delayed bifurcations

T2 - the case of additive white noise

AU - Stocks, N. G.

AU - Mannella, R.

AU - McClintock, Peter V. E.

PY - 1989/11/1

Y1 - 1989/11/1

N2 - The influence of additive white noise on the delay of a bifurcation point in the presence of a swept control parameter has been studied by analog experiment and digital simulation. Measurements of the time taken for the second moment [x^2(t)] to reach a given threshold are in excellent agreement with the calculations of Zeghlache, Mandel, and Van den Broeck [Phys, Rev. A 40, 286 (1989)). It is demonstrated, however, that the mean first-passage time (MFPT) for x^2(t) to attain the same threshold, corresponding to the quantity that is usually determined in laser experiments, can be markedly different. It may be either larger or smaller, depending on the conditions under which the measurements are made. A calculation of the MFPT is presented and shown to be in excellent agreement with the experimental measurements and to reduce, in the relevant limit, to the theoretical results previously published by Torrent and San Miguel [Phys. Rev. A 38, 245 (1988)].

AB - The influence of additive white noise on the delay of a bifurcation point in the presence of a swept control parameter has been studied by analog experiment and digital simulation. Measurements of the time taken for the second moment [x^2(t)] to reach a given threshold are in excellent agreement with the calculations of Zeghlache, Mandel, and Van den Broeck [Phys, Rev. A 40, 286 (1989)). It is demonstrated, however, that the mean first-passage time (MFPT) for x^2(t) to attain the same threshold, corresponding to the quantity that is usually determined in laser experiments, can be markedly different. It may be either larger or smaller, depending on the conditions under which the measurements are made. A calculation of the MFPT is presented and shown to be in excellent agreement with the experimental measurements and to reduce, in the relevant limit, to the theoretical results previously published by Torrent and San Miguel [Phys. Rev. A 38, 245 (1988)].

U2 - 10.1103/PhysRevA.40.5361

DO - 10.1103/PhysRevA.40.5361

M3 - Journal article

VL - 40

SP - 5361

EP - 5369

JO - Physical review a

JF - Physical review a

SN - 1050-2947

IS - 9

ER -