Kuramoto Model of Nonlinear Coupled Oscillators as a Way for Understanding Phase Synchronization: Application to Solar and Geomagnetic Indices |
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| Authors: | Elena M Blanter Jean-Louis Le Mouël Mikhail G Shnirman Vincent Courtillot |
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| Institution: | 1. Institut de Physique du Globe, Paris, France
2. Institute of Earthquake Prediction Theory and Mathematical Geophysics, RAS, Moscow, Russia
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| Abstract: | We apply a Kuramoto model of nonlinear coupled oscillators to the simulation of slow variations of the phase difference between sunspot number R I ] and geomagnetic indices aa and ζ]. The Kuramoto model is described for the particular case of two oscillators connected by symmetric coupling with quasi-stationary behavior, and its properties are investigated. By solving an inverse problem, we reconstruct the evolution of the couplings between pairs of indices R I and aa, R I and ζ, aa and ζ], and interpret these in terms of the physics of the solar dynamo. The de-correlation between R I and geomagnetic indices found in Solar Cycle 20 by Le Mouël et al. (J. Geophys. Res. 117, A09103, 2012) is successfully reproduced by the Kuramoto model and corresponds to the alternation of the leading oscillator. Application of the Kuramoto model to the cross-correlations C(R I ,ζ) and C(aa,ζ)] for ζ-indices computed in eight geomagnetic stations shows the latitudinal dependence of the mean phase difference. We discuss these results in terms of the solar-wind contribution to local geomagnetic indices ζ]. |
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