Nonlinear and chaotic resonances in solar activity

TL;DR

This paper analyzes sunspot data revealing a 3.7-year periodicity linked to subharmonic resonance, chaos, and solar rotation, providing new insights into the complex dynamics of solar activity.

Contribution

It demonstrates the presence of nonlinear and chaotic resonances in solar activity, connecting spectral decay, Lyapunov exponents, and solar rotation periods.

Findings

Identification of a 3.7-year periodicity in sunspot data

Evidence of chaos through exponential spectral decay and Lyapunov exponents

Link between subharmonic resonance and solar active longitude flip-flop

Abstract

It is shown that, the wavelet regression detrended fluctuations of the monthly sunspot number for 1749-2009 years exhibit strong periodicity with a period approximately equal to 3.7 years. The wavelet regression method detrends the data from the approximately 11-years period. Therefore, it is suggested that the one-third subharmonic resonance can be considered as a background for the 11-years solar cycle. It is also shown that the broad-band part of the wavelet regression detrended fluctuations spectrum exhibits an exponential decay that, together with the positive largest Lyapunov exponent, are the hallmarks of chaos. Using a complex-time analytic approach the rate of the exponential decay of the broad-band part of the spectrum has been theoretically related to the Carrington solar rotation period. Relation of the driving period of the subharmonic resonance (3.7-years) to the active longitude flip-flop phenomenon, in which the dominant part of the sunspot activity changes the longitude every 3.7 years on average, has been briefly discussed.