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Two regimes in the regularity of sunspot number
Alexander Shapoval, Jean-Louis Le Mouël, Vincent Courtillot, M. Shnirman, 2013, izvirni znanstveni članek

Opis: Sunspot numbers WN display quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional λ (an "irregularity index") that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to work with sunspot numbers. We compute λ for the daily WN from 1850 to 2012 within 4 yr sliding windows: λ exhibit sharp maxima at solar minima and secondary maxima at solar maxima. This pattern is reflected in the ratio R of the amplitudes of the main versus secondary peaks. Two regimes have alternated in the past 150 yr, R1 from 1850 to 1915 (large λ and R values) and R2 from 1935 to 2005 (shrinking difference between main and secondary maxima, R values between 1 and 2). We build an autoregressive model consisting of Poisson noise plus an 11 yr cycle and compute its irregularity index. The transition from R1 to R2 can be reproduced by strengthening the autocorrelation a of the model series. The features of the two regimes are stable for model and WN with respect to embedding dimension and delay. Near the time of the last solar minimum (~2008), the irregularity index exhibits a peak similar to the peaks observed before 1915. This might signal a regime change back from R2 to R1 and the onset of a significant decrease of solar activity.
Ključne besede: Lyapunov exponent, solar activity, solar cycle
Objavljeno v RUNG: 19.04.2021; Ogledov: 1969; Prenosov: 59
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Reconstruction of the coupling between solar proxies : when approaches based on Kuramoto and Van der Pol models agree with each other
Anton Savostianov, Alexander Shapoval, M. Shnirman, 2020, izvirni znanstveni članek

Opis: The objective of this paper is to establish that algorithms, which reconstruct the coupling between solar proxies based on the properties of the Kuramoto equations, and algorithms, based on the van der Pol equations, might produce similar estimates. To this end, the inverse problem is formulated as follows: reconstruct the coupling based on the solutions of the corresponding equations. For either system of the equations we construct an algorithm solving the inverse problem and establish that there exists a range of moderate values of the correlation such that the algorithms produce practically identical coupling within the established range. The lower boundary of this range is dependent on the half-difference of the oscillators’ frequencies. Then, we apply the two reconstruction algorithms to solar index ISSN and the geomagnetic index aa, which are proxies to the toroidal and poloidal magnetic fields of the Sun respectively. Their correlation belongs within the range that yields the proximity of the coupling reconstructed with all solar cycles from 11 till 23 except 20 and, possibly, 21. Our finding relate the reconstruction of characteristics of solar activity inferred by Blanter et al [Sol. Phys. 2014, 289, 4309; Sol. Phys. 2016, 291, 1003] from the Kuramoto model to the state of the art solar dynamo theory based on the magnetohydrodynamic equations.
Ključne besede: coupled oscillators, synchronization, solar activity
Objavljeno v RUNG: 22.03.2021; Ogledov: 2106; Prenosov: 0
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