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Hopf bifurcations with fluctuating gain
Author(s) -
Triana S.A.,
Kelley D.H.,
Zimmerman D.,
Sisan D.,
Lathrop D.P.
Publication year - 2008
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.200811012
Subject(s) - instability , hopf bifurcation , white noise , physics , noise (video) , bifurcation , turbulence , steady state (chemistry) , intensity (physics) , mechanics , statistical physics , mathematics , optics , nonlinear system , quantum mechanics , chemistry , statistics , image (mathematics) , artificial intelligence , computer science
A Hopf bifurcation describes a transition from a steady state to an oscillatory one. This report describes how the presence of white Gaussian noise in the term driving the instability (the gain) affects the character of such a transition. We find that for small noise intensities the effective critical value of the bifurcation parameter increases linearly with the noise intensity. This result is used to quantitatively describe the onset of the magneto‐rotational instability in a laboratory experiment using liquid metal with turbulent background flow. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)