DYNAMICS OF WOLF NUMBERS AND STRUCTURAL FUNCTIONS OF KOLMOGOROV

Vysotskaya Anna Arkadievna, Pronina Elena Nikolaevna

One of the features of the Sun is almost-periodic, regular changes in various manifestations of solar activity. The most well-known phenomenon is sunspots, areas with a strong magnetic field and low temperature, the number of which is determined by Wolf numbers. The study of solar activity and the prediction of its changes are of great interest for various fields of knowledge, for example, for describing the future, current and past state of the atmosphere. Kolmogorov’s structural functions make it possible to identify the periodic components of the process, which makes it possible to make effective systemic forecasts. The article is devoted to the analysis of the features of Kolmogorov's structural functions. The apparatus of structural functions is a tool for studying random processes with stationary increments. On the example of the dynamics of Wolf numbers, it is shown that two qualitatively different ranges are distinguished in the structure functions. In the first, the scale dependence of the structure function follows a power law. Here the self-similarity property is realized. Oscillating components are observed in the second range. In this case, the boundaries of self-similarity are interconnected with the position of local minima of the structural function, by which almost-periods of oscillations are determined. Therefore, to reveal hidden periodicities, all features of structural functions turn out to be significant: the boundaries of scale invariance ranges, points of phase change, maxima and minima.

Keywords:processes with stationary increments, structural function, scaling, almost-period, Wolf’s numbers