Nonlinear Dynamics Recognition in Solar Time Series Based on Recurrence Plot Techniques

Recurrence is a fundamental property of many nonlinear dynamical systems, which can be exploited to characterize such dynamical system´s intrinsically behaviour in the phase space. The recurrence plot is a powerful and sensitive approach to quantify the nonlinear interaction of the two complex systems due to their coupling. As an example of typical data sets where the recurrence based methods have proven powerful, we apply two modern nonlinear approaches, including cross-recurrence plot and line of synchronization, to analyze the phase asynchrony between coronal index and sunspot numbers during the time interval from January 1939 to December 2008. It is found that, (1) the average value of their phase lags is about -10 months, implying that coronal index lags behind sunspot numbers during the considered time interval, (2) their phase relationship is not a simply linear relation, although they are highly correlated with each other. Our analysis results indicate that modern nonlinear approaches for the phase analysis between different time series are fairly useful and powerful.