Calculating Correlation Dimension for Chaotic Time Series

The following MATLAB program calculates the correlation dimension for chaotic time series. The implementation follows these computational steps: The program begins by reading time series data and performing necessary preprocessing, which may include normalization or noise reduction to ensure data quality for subsequent analysis. It then estimates optimal time delay and embedding dimension parameters using established methods such as mutual information for delay calculation and false nearest neighbors for dimension determination. Based on the estimated parameters, the program reconstructs the phase space using time-delay embedding technique, creating multidimensional vectors that capture the underlying system dynamics. The core algorithm implements the Grassberger-Procaccia method to compute correlation dimension by calculating the correlation integral across multiple scaling regions. The code includes adjustable parameters such as the number of embedding dimensions to test, maximum time delay, and scaling range selection. Key functions utilized include vectorized distance calculations for efficient computation of pairwise distances in phase space, and logarithmic scaling analysis to determine the slope of the correlation integral curve. It's important to note that the output results require proper interpretation and additional analysis to fully understand the correlation dimension characteristics of the chaotic time series. The program provides both numerical results and visualization options for validation purposes.