Investigation of Chaotic Nature of Sunspot Data by Nonlinear Analysis Techniques

In this work, an attempt is made to detect the chaotic nature of smooth monthly sunspot (SSN) time series using various nonlinear analysis techniques to quantify the uncertainty involved. Different nonlinear dynamic methods, with varying levels of complexity, are employed such as average mutual information and embedding dimension method to construct a phase space. The correlation dimension method is used to identify the minimum number of variables required to forecast and the Lyapunov exponent method is used to confirm the presence of chaos and the maximal Lyapunov exponent is used to calculate the predictable time. These methods provide either direct or indirect identification of chaotic behavior in the sunspot number. From the analysis results, we arrive at a conclusion that the dynamical behavior of SSNs is a low-dimensional chaotic attractor and the solar activity is a chaotic phenomenon but not a stochastic behavior. It can be inferred that SSN is deterministic; hence, long term prediction of the SSN is impossible.