An Interdisciplinary Journal

2004, Vol.7, No.3, pp.210-226

Dinara`s Crosses, Chaoticity and Robustness in Stochastic Dynamics of Solar Activity.
R. M. Yulmetyev, S. A. Demin, P. Hänggi, A. I. Galeev

The dynamics of stochastic processes in real complex systems is very complicated and entangled. At the examination of various dynamic states of similar systems one of the central points is consisted in finding a quantitative measure of chaoticity and regularity in its evolution. In this work we represent the results of the study of solar activity from the point of view of complexity, discreteness, non-stationarity and non-Markovity of dynamic evolution of atmosphere of the Sun. The study was carried out by using of means of the statistical theory of discrete non-Markov stochastic processes [1]-[3]. The statistical non-Markov effects in time series of solar activity are considered thoroughly. For realization of correlation analysis as an initial time series we use a time series of Wolf number (one of solar indexes). In this work the effects of regularity and chaoticity connected with dynamics of various cycles of solar activity come to light. For the finding of local time dependence the kinetic and relaxation parameters and obtaining of the additional information about physical nature of the phenomena going on the Sun we offers local averaging operation. In this paper the comparative analysis of the various parameters connected with minima and maxima of solar activity has been implemented. Specific features in behavior of phase clouds at a minimum of solar activity are characterized by the occurrence of obtuse angles and symbolical "Dinara's Crosses" in distribution of phase points. The phase points at a maximum of solar activity form a nucleus in the form of the oval curve. The dynamics of solar spots is connected to specific alternation of the effects of chaoticity and robustness. The peculiarities of the frequency dependence of non-Markovity parameter which is the original indicator of chaoticity and regularity reveal a complicated competition of noise and separate modes of the Sun mobility.
Key words: solar activity, chaoticity, random processes, discreteness, non-Markovity

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