Development of a new approach to data analysis of complex systems: study of synchronization in the dynamics of solar activity parameters

In this paper, we develop a new approach to the study of matching and mismatching effects in simultaneously recorded time signals characterizing the evolution of natural systems. We discuss the challenges of developing methods of intellectual data analysis of data generated by complex composite objects. In the framework of basic provisions and concepts of Flicker-Noise Spectroscopy, we study the frequency-phase synchronization in the dynamics of Wolf numbers and coronal solar ejections. The evolution of collective processes in the solar atmosphere is represented by changes in the shape of the cross-correlators. We calculated the quantitative structural parameters of cross-correlators to assess causal relationships between the parameters of solar activity. The established levels of cross-correlations in thermodynamically open distributed systems, such as the Sun, can become an object of standardization. The combination of Flicker-Noise Spectroscopy with mathematical models and machine learning software will allow advancing in understanding the collective phenomena realized in complex systems.