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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -