Is a sudden increase of irregularity of sunspot numbers a precursor of a return to low solar activity?

Journal of Geophysical Research. 2014. Vol. 119. P. 6120–6130.

Shapoval A., Le Mouel J. -., Shnirman M. G., Courtillot V.

We have recently introduced an irregularity index λ for daily sunspot numbers ISSN, derived from the well-known Lyapunov exponent, that attempts to reflect irregularities in the chaotic process of solar activity. Like the Lyapunov exponent, the irregularity index is computed from the data for different embedding dimensions m (2-32). When m = 2, λ maxima match ISSN maxima of the Schwabe cycle, whereas when m = 3, λ maxima occur at ISSN minima. The patterns of λ as a function of time remain similar from m = 4 to 16: the dynamics of λ change between 1915 and 1935, separating two regimes, one from 1850 to 1915 and the other from 1935 to 2005, in which λ retains a similar structure. A sharp peak occurs at the time of the ISSN minimum between cycles 23 and 24, possibly a precursor of unusual cycle 24 and maybe a new regime change. λ is significantly smaller during the ascending and descending phases of solar cycles. Differences in values of the irregularity index observed for different cycles reflect differences in correlations in sunspot series at a scale much less than the 4-yr sliding window used in computing them; the lifetime of sunspots provides a source of correlation at that time scale. The burst of short-term irregularity evidenced by the strong l-peak at the minimum of cycle 23-24 would reflect a decrease in correlation at the time scale of several days rather than a change in the shape of the cycle.

Keywords: sunspots, regime changes, autoregression