C-C Algorithm for Chaotic Time Series Analysis

Chaotic time series analysis serves as a fundamental method for studying nonlinear dynamical systems. The C-C algorithm, as a crucial phase space reconstruction technique, effectively determines optimal delay time and embedding dimension parameters. This algorithm computes the correlation integral of time series to identify optimal reconstruction parameters, laying the foundation for subsequent chaotic identification and prediction tasks.

In MATLAB implementation, the C-C algorithm first requires standardization of the original time series to eliminate dimensional influences. The core implementation involves calculating correlation integrals under different combinations of delay times and embedding dimensions, followed by plotting statistical quantity curves. The algorithm's key innovation lies in identifying the first minimum point or stable value point on these curves, where the corresponding parameters represent the optimal delay time. The MATLAB code typically utilizes functions like xcorr for autocorrelation calculations and meshgrid for parameter space exploration.

Compared to traditional autocorrelation methods, the C-C algorithm simultaneously considers nonlinear characteristics of time series, avoiding subjective threshold setting. Its MATLAB implementation commonly incorporates optimization strategies such as data segmentation and multi-grid search to balance computational accuracy and efficiency. The algorithm proves particularly suitable for analyzing short, noise-containing experimental chaotic signals, with practical code implementations often featuring parallel computing techniques for handling large parameter spaces.