×

zbMATH — the first resource for mathematics

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.
MSC:
85A15 Galactic and stellar structure
78A25 Electromagnetic theory, general
76W05 Magnetohydrodynamics and electrohydrodynamics
35R30 Inverse problems for PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Acebrón, J. A.; Bonilla, L. L.; Vicente, C. J.P.; Ritort, F.; Spigler, R., The kuramoto model: A simple paradigm for synchronization phenomena, Rev Modern Phys, 77, 1, 137-185 (2005)
[2] Bick C, Goodfellow M, Laing CR, Martens EA. Understanding the dynamics of biological and neural oscillator networks through mean-field reductions: a review. arXiv:1902.05307, 2019.
[3] Blanter, E. M.; Le Mouël, J.-L.; Shnirman, M. G.; Courtillot, V., Kuramoto model of nonlinear coupled oscillators as a way for understanding phase synchronization: application to solar and geomagnetic indices, Solar Phys, 289, 11, 4309-4333 (2014)
[4] Blanter, E. M.; Le Mouël, J.-L.; Shnirman, M. G.; Courtillot, V., Kuramoto model with non-symmetric coupling reconstructs variations of the solar-cycle period, Solar Phys, 291, 3, 1003-1023 (2016)
[5] Blanter, E. M.; Le Mouël, J.-L.; Shnirman, M. G.; Courtillot, V., Reconstruction of the north-south solar asymmetry with a kuramoto model, Solar Phys, 292, 4 (2017)
[6] Brun, AS; Browning, MK; Dikpati, M.; Hotta, H.; Strugarek, A., Recent advances on solar global magnetism and variability, Space Sci Rev, 196, 1-4, 101-136 (2015)
[7] Charbonneau, P., Multiperiodicity, chaos, and intermittency in a reduced model of the solar cycle, Solar Phys, 199, 2, 385-404 (2001)
[8] Charbonneau, P., Solar dynamo theory, Ann Rev Astron Astrophys, 52, 251-290 (2014)
[9] Chen, R.; Zhao, J., A comprehensive method to measure solar meridional circulation and the center-to-limb effect using time-distance helioseismology, Astrophys J, 849, 2, 144 (2017)
[10] Choudhuri, A. R., A critical assessment of the flux transport dynamo, J Astrophys Astron, 36, 1, 5-14 (2015)
[11] Choudhuri, A. R., Flux transport dynamo: From modelling irregularities to making predictions, J Atmos Solar-Terr Phys, 176, 5-9 (2018)
[12] Cordshooli, G. A.; Vahidi, A., Phase synchronization of van der pol-duffing oscillators using decomposition method, Adv Studies Theor Phys, 3, 429-437 (2009) · Zbl 1187.37043
[13] Enjieu Kadji, H. G.; Yamapi, R., General synchronization dynamics of coupled van der pol-duffing oscillators, Physica A, 370, 2, 316-328 (2006)
[14] Featherstone, N. A.; Miesch, M. S., Meridional circulation in solar and stellar convection zones, Astrophys J, 804, 1, 67 (2015)
[15] Hathaway, D. H., The solar cycle, Living Rev Solar Phys, 12, lrsp-4 (2015)
[16] Hathaway, D. H.; Upton, L. A., Predicting the amplitude and hemispheric asymmetry of solar cycle 25 with surface flux transport, J Geophys Res, 121, 11, 10-744 (2016)
[17] Hazra, G.; Choudhuri, A. R., Explaining the variation of the meridional circulation with the solar cycle, Proc Int Astron Union, 13, S340, 313-316 (2018)
[18] Hazra, G.; Karak, B. B.; Choudhuri, A. R., Is a deep one-cell meridional circulation essential for the flux transport solar dynamo?, Astrophys J, 782, 2, 93 (2014)
[19] Jiang, J., State-of-the-art of kinematic modeling the solar cycle, Proc Int Astron Union, 13, S340, 269-274 (2018)
[20] Karak, B. B.; Miesch, M., Solar cycle variability induced by tilt angle scatter in a babcock-leighton solar dynamo model, Astrophys J, 847, 1, 69 (2017)
[21] Kuznetsov, A. P.; Stankevich, N. V.; Turukina, L. V., Coupled van der pol-duffing oscillators: phase dynamics and structure of synchronization tongues, Physica D, 238, 14, 1203-1215 (2009) · Zbl 1191.34068
[22] Lopes, I.; Passos, D.; Nagy, M.; Petrovay, K., Oscillator models of the solar cycle, Space Sciences Series of ISSI, 535-559 (2015), Springer New York
[23] Mayaud, P.-N., The aa indices: a 100-year series characterizing the magnetic activity, J Geophys Res, 77, 34, 6870-6874 (1972)
[24] Miesch, M. S.; Dikpati, M., A three-dimensional babcock-leighton solar dynamo model, Astrophys J Lett, 785, 1, L8 (2014)
[25] Mininni, P. D.; Gomez, D. O.; Mindlin, G. B., Simple model of a stochastically excited solar dynamo, Solar Phys, 201, 2, 203-223 (2001)
[26] Passos, D.; Charbonneau, P.; Miesch, M., Meridional circulation dynamics from 3d magnetohydrodynamic global simulations of solar convection, Astrophys J Lett, 800, 1, L18 (2015)
[27] Pesnell, W. D., Predictions of solar cycle 24: How are we doing?, Space Weather, 14, 1, 10-21 (2016)
[28] Pesnell, W. D.; Schatten, K. H., An early prediction of the amplitude of solar cycle 25, Solar Phys, 293, 7, 112 (2018)
[29] Petrovay, K., Solar cycle prediction, Living Rev Solar Phys, 7, 1, 6 (2010)
[30] Pikovsky, A.; Rosenblum, M.; Kurths, J., Synchronization: a universal concept in nonlinear sciences, 12 (2003), Cambridge university press · Zbl 1219.37002
[31] Rajasekar, S.; Murali, K., Resonance behaviour and jump phenomenon in a two coupled duffing-van der pol oscillators, Chaos Solitons Fractals, 19, 4, 925-934 (2004) · Zbl 1058.34048
[32] Sello S. Solar cycle activity: an early prediction for cycle# 25. arXiv:1902.05294, 2019.
[33] SILSO World Data Center, The International Sunspot Number, International Sunspot Number Monthly Bulletin and online catalogue (1880-2016)
[34] Strogatz, SH, From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena, 143, 1-4, 1-20 (2000) · Zbl 0983.34022
[35] Svalgaard, L.; Cliver, E. W.; Kamide, Y., Sunspot cycle 24: Smallest cycle in 100 years?, Geophys Res Lett, 32, 1 (2005)
[36] Turner, D. C.; Ladde, G. S., Stochastic modelling, analysis, and simulations of the solar cycle dynamic process, Astrophys J, 855, 2, 108 (2018)
[37] Usoskin, I. G., A history of solar activity over millennia, Living Rev Solar Phys, 14, 1, 3 (2017)
[38] Wang, Y-M, Surface flux transport and the evolution of the sun’s polar fields, Space Sci Rev, 210, 1-4, 351-365 (2017)
[39] Zhao, J.; Bogart, R. S.; Kosovichev, A. G.; Duvall, T. L.; Hartlep, T., Detection of equatorward meridional flow and evidence of double-cell meridional circulation inside the sun, Astrophys J, 774, 2, L29 (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.