Identifying the quasi-regular and stochastic components of solar cyclicity and their properties

We have averaged over every Carrington semi-rotation (C.s.-r.), the daily Wolf numbers (RW), total areas of sunspot groups (SA), the 10.7-cm radio flux (F _10.7), and the modulus of the mean magnetic field (|SMMF|). The fractal method of scaling the variance of time series was used to separate the regular and stochastic components. The manifestation of chaotic and stochastic properties of these components was investigated by testing with the methods of chaotic dynamics, as well as with two new methods: (1) close return maps; and (2) multivariate scaling analysis. Results: (1) by separating time series of global indices of solar activity, it is possible to identify the quasi-regular (the quasi-regularity is caused not by the absolute smoothness of the function) component on time scales longer than two years, and the irregular component on time scales shorter than two years; (2) the regular component has the properties of a nonlinear quasi-periodic oscillator; (3) the irregular component is a random one and has the properties of chromatic noise; and (4) by investigating the nonlinear connection of the solar activity indices under consideration it was found that such a connection is strong between F _10.7and RW. A nonlinear correlation between the attractors RW–|SMMF| and F _10.7–|SMMF| was also revealed.