C-C Algorithm Utilizing Correlation Integral for Simultaneous Estimation of Time Delay and Embedding Dimension

In this paper, we discuss the application of the C-C algorithm in phase space reconstruction and the significance of correlation integrals. The C-C algorithm not only estimates time delay parameters but also determines optimal embedding dimensions simultaneously. This methodology finds extensive applications in analyzing chaotic time series data. Our implementation specifically applies the C-C algorithm to compute both time delay and embedding dimension parameters for chaotic time series generated by the Duffing equation, further validating the algorithm's effectiveness in phase space reconstruction tasks. The computational approach involves calculating correlation integrals across different delay parameters and dimension choices to identify optimal reconstruction parameters. We also explore potential applications of the C-C algorithm in other domains and propose future research directions for enhancing its computational efficiency and expanding its applicability to complex dynamical systems.