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Stochastic resonance in a bistable geodynamo model
Author(s) -
Lorito S.,
Schmitt D.,
Consolini G.,
De Michelis P.
Publication year - 2005
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.200410381
Subject(s) - dynamo , dynamo theory , physics , stochastic resonance , multiplicative function , bistability , amplitude , earth's magnetic field , multiplicative noise , statistical physics , magnetic field , mathematical analysis , mathematics , noise (video) , quantum mechanics , signal transfer function , digital signal processing , artificial intelligence , computer science , analog signal , electrical engineering , image (mathematics) , engineering
Recently a signal with a period of 100 kyr in the distribution of residence times between reversals of the geomagnetic field has been suggested as signature of stochastic resonance. Here we test this suggestion by applying periodic modulations to a model of the geodynamo as a bistable oscillator, where stochastic fluctuations of the induction effect (multiplicative noise) lead to random transitions between the two polarity states of the supercritically excited fundamental axial dipole mode. By adding a weak periodic component either to the dynamo effect (multiplicative periodic term) or as a source term to the dynamo equation (additive periodic term) we demonstrate stochastic resonance. Depending on the multiplicative (additive) character of the periodic term, we find peaks at integer (half‐integer) values of the applied period, superimposed on the otherwise Poissonian distribution of residence times. Especially the optimum resonance conditions for various mean times between reversals and various periodicities are derived. The periodic terms need to be about 0.1 in amplitude compared to the other terms in the dynamo equation to show the observed signatures of the magnetic field of the Earth. A sharp peak at the forcing frequency in the power spectrum of the dipole amplitude is only found in the additive case. As such a peak is absent in the Earth data, this rules for the multiplicative case. It is yet unclear what may cause such an effect to the geodynamo. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)