Analysis of chaotic features and modelling of sunspot cycle

The nature of solar activity and the processes that cause it are not yet fully understood. However, developing technology is becoming more and more vulnerable to the effects of space weather, where the main source is the sun. In this study, phase space analysis, Hurst exponential and correlation dimension techniques were applied to sunspot number time series in order to investigate the chaotic dynamics of solar activity. In the phase space analysis, the attractor formations which are representative of the chaotic processes are encountered. The calculated value of Hurst exponent (0.86) reveals that the examined time series has a high level of long-term memory which is also an expected feature of chaotic processes. As a result of the studies made by correlation dimension technique, it is determined that there are 6 different processes affecting the sunspot numbers. Empirical Dynamic Modelling is a new approach to modelling and predicting systems that underlying processes are not fully defined. Instead of a set of equations used to model a system, in this method patterns are searched and used by analyzing time series of a system variable. This approach was applied to sunspot number time series and the prediction results were consisted with observed values of the last five sunspot cycles (20, 21, 22, 23 and 24). In addition, a new parameter (prediction starting point) has been defined that improves the performance of an extrapolation algorithm (Simplex Projection) which is very popular in solar cycle predictions. Using this new parameter, a prediction for the 25th sunspot cycle was created. According to this prediction, it is expected that the next cycle will be a double peaked cycle. The first maximum is expected to occur between February and May 2024 with smoothed monthly mean sunspot number between 70-100. The second maximum is expected to occur between November 2025 and February 2026 with smoothed monthly mean sunspot number between 87-93. KEYWORDS: Chaos, Non-linear methods, Prediction, Solar Cycle, Space Weather