Influence of the Gleissberg Cycle on Variations of the 11-Year Cycle of Solar Activity in 1700–2021

The wavelet analysis was used to study the spectral composition of the sunspot numbers SN during 1700–2021. In addition to the dominant 11-year component, two powerful components of the Gleissberg cycle can be traced in the spectrum: before 1880, a branch with a period of ~60 years; from 1850 a branch of ~115 years is found. It is found that the series of lengths and amplitudes of the solar cycle as a whole are inversely related (correlation coefficient k = –0.5–0.63). The interval between the series at which the maximum anticorrelation is reached depends on time. In the 18th and early 19th centuries, the lag was equal to one cycle, in the 19th century it was two cycles, and from 1950 to our time the lag decreased to 2 years. Quasi-periodic structures, which are typical for long periods of low solar activity, have been identified. Such a spectral feature in ~1800 (Dalton minimum) was caused by the influence of the 60-year branch, while the one that has been forming since the beginning of the 21st century is due to the weaker influence of the circa-centenary branch. Therefore, it should be expected that the next solar cycles will be higher and shorter than during the period of the Dalton minimum. It has been shown that solar cycle length variations for the last 321 years can be described within the framework of the model, which is an 11-year oscillation that is subject to frequency modulation by the branches of the Gleisberg cycle (60 and 115 years) with time-varying influences of the modulator.