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This paper provides a comprehensive review of methods for selecting optimal delay time interval and embedding dimension in phase space reconstruction of chaotic time series. It introduces the false nearest neighbors method that simultaneously considers both parameters, along with a minimum prediction error approach for parameter optimization.
The C-C algorithm employs correlation integrals to simultaneously estimate time delay and embedding dimension, serving as the foundation for phase space reconstruction. This implementation computes time delay and embedding dimension parameters for chaotic time series generated by the Duffing equation using the C-C methodology, demonstrating practical application through computational implementation.
Implementation of CC Algorithm for Determining Optimal Delay Time and Embedding Dimension in Time Series Phase Space Reconstruction
Implementation of GP Algorithm to Determine Optimal Embedding Parameters (Dimension and Delay Time) for Time Series Phase Space Reconstruction
This program calculates both time delay t and embedding dimension m simultaneously, offering a more efficient alternative to conventional autocorrelation function and GP methods. The algorithm is particularly useful for Lyapunov exponent computation where both parameters need to be determined beforehand. The implementation involves phase space reconstruction techniques and mutual information optimization for optimal parameter selection.
Determining Embedding Dimension for Duffing Equation via CAO Method - A Computational Approach with Algorithm Implementation
Implementation of Grassberger-Procaccia Algorithm for Determining Optimal Parameters in Nonlinear Time Series Analysis
C-C Method Implementation for Time Delay and Embedding Dimension Calculation in Nonlinear Time Series Analysis
Grassberger-Procaccia Method Implementation for Correlation Dimension and Embedding Dimension Estimation in Chaotic Systems