Subharmonic and chaotic resonances in solar activity

¹ ICAR - P.O. Box 31155, Jerusalem 91000, Israel
² ICTP - Strada Costiera 11, I-34151 Trieste, Italy, EU

Received: 27 June 2010
Accepted: 23 November 2010

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.