Estimation of chaotic nature of dynamical system through nonlinear analysis

Estimation of low-dimensional chaos from nonlinear time series is a very important but difficult task in scientific fields. Among the several techniques proposed for this aim are the rescaled range analysis and maximal Lyapunov exponent, which quantify the amount of a time series. These two techniques are applied to analyse the astronomical time series, which is non-stationary and nonlinear in nature. It is found that, (1) solar activity exhibits a complex and strongly chaotic behaviour and is governed by a low-dimensional chaotic attractor; (2) the predictability time of the chaotic motion in solar-activity indicator is up to 1.12 years. These results indicate that chaotic characteristics obviously exist in the solar time series, and thus techniques based on rescaled range analysis and maximal Lyapunov exponent can be used to analyse and predict solar activity. It should be pointed out that solar activity forecast should be done only for a short to medium term due to the initial value of the sensitive of the chaotic system.