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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. (English) Zbl 07265155
Summary: 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 E. M. Blanter et al. [“Kuramoto model of nonlinear coupled oscillators as a way for understanding phase synchronization: application to solar and geomagnetic indices”,Solar Phys. 289, No. 11, 4309–4333 (2014; doi:10.1007/s11207-014-0568-9); “Kuramoto model with non-symmetric coupling reconstructs variations of the solar-cycle period”, Solar Phys. 291, No. 3, 1003–1023 (2016; doi:10.1007/s11207-016-0867-4)] from the Kuramoto model to the state of the art solar dynamo theory based on the magnetohydrodynamic equations.
85A15 Galactic and stellar structure
78A25 Electromagnetic theory, general
76W05 Magnetohydrodynamics and electrohydrodynamics
35R30 Inverse problems for PDEs
Full Text: DOI
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