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## Two Regimes in the Regularity of Sunspot Number

Sunspot number *WN* displays quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional l (an “irregularity index”) that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to work with sunspot numbers. We compute l for the daily *WN* from 1850 to 2012 within 4-year sliding windows: l exhibit sharp maxima at solar minima and secondary maxima at solar maxima. This pattern is reflected in the ratio *R* of the amplitudes of the main vs secondary peaks. Two regimes have alternated in the past 150 years, R1 from 1850 to 1915 (large l and *R* values) and R2 from 1935 to 2005 (shrinking difference between main and secondary maxima, *R* values between 1 and 2). We build an autoregressive model consisting of Poisson noise plus an 11-yr cycle, and compute its irregularity index. The transition from R1 to R2 can be reproduced by strengthening the autocorrelation *a *of the model series. The features of the two regimes are stable for model and *WN* with respect to embedding dimension and delay. Near the time of the last solar minimum (~2008), the irregularity index exhibits a peak similar to the peaks observed before 1915. This might signal a regime change back from R2 to R1 and the onset of a significant decrease of solar activity.