Dynamical analysis of long-term solar activity based on ensemble empirical mode decomposition

This is the authors' abstract. We don't add key points for this paper.

Long-term solar activity, including the Schwabe cycle, exhibits the dynamics of a low-dimensional strange attractor based on sunspot numbers. In contrast, long-term solar activity exhibits randomness when using proxies like ¹⁴C and ¹⁰Be. To investigate these differing results and understand the interaction of various frequency components in the phase space of long-term solar activity, we use ensemble empirical mode decomposition and phase space reconstruction on direct solar observational data, including international and group sunspot numbers, to obtain components displaying different frequencies and their phase spaces. The phase space of the single-frequency component of sunspot numbers shows a clear fixed point around which the phase trajectory rotates over time. The phase space of long-term solar activity resembles a cone, with a fixed point near the origin at its apex. Phase trajectories rotate around this fixed point, completing one rotation per solar cycle. When the 11-yr cycle is removed, the phase trajectories lack a fixed point and drift, consistent with the reconstructed phase space of the first-order autoregressive model. Furthermore, the phase portrait of component C₈ of the Rössler system’s z variable resembles the Schwabe cycle component of solar activity. Consequently, the 11-yr cycle substantially impacts the phase space of long-term solar activity. When the 11-yr cycle is removed, the long-term solar activity at lower frequencies appears random. Compared to the Rössler system, the dynamic characteristics of long-term solar activity are more intricate.