Chaotic Time Series Characteristics with G-P Algorithm for Correlation Dimension Calculation

In this article, we explore the characteristics of chaotic time series and demonstrate how to calculate correlation dimension using the G-P (Grassberger-Procaccia) algorithm. We provide detailed MATLAB implementation guidelines, including key functions for phase space reconstruction and correlation integral calculation. The implementation involves creating delay coordinates using the embed function and computing correlation sums through vectorized operations for optimal performance. We discuss the step-by-step computational process of the G-P algorithm, including embedding dimension selection, distance matrix calculation, and scaling region identification. Additionally, we analyze the algorithm's advantages in handling nonlinear systems and its limitations regarding data requirements and computational complexity. We propose improvement methods such as adaptive radius selection and parallel computing implementation to enhance calculation precision. The article includes practical code examples for data visualization using MATLAB's plotting functions to better interpret and present results. This work aims to provide valuable insights for chaotic time series research and offer inspiration to researchers in related fields.