Long-term solar cycle evolution: Review of recent developments

The sunspot number series forms the longest directly observed index of solar activity and allows one to trace its variations on the time scale of about 400 years since 1610. This time interval covers a wide range from seemingly vanishing sunspots during the Maunder minimum in 1645-1700 to the very high activity during the last 50 years. Although the sunspot number series has been studied for more than a century, new interesting features have been found even recently. This paper gives a review of the recent achievements and findings in long-term evolution of solar activity cycles such as determinism and chaos in sunspot cyclicity, cycles during the Maunder minimum, a general behaviour of sunspot activity during a great minimum, the phase catastrophe and the lost cycle in the beginning of the Dalton minimum in 1790s and persistent 22-year cyclicity in sunspot activity. These findings shed new light on the underlying physical processes responsible for sunspot activity and allow a better understanding of such empirical rules as the Gnevyshev-Ohl rule and the Waldmeier relations.