Determining Embedding Dimension for Rossler System Using Mutual Information Derived Time Delay Combined with Cao's Method

This research employs time delay derived from mutual information method combined with Cao's method to determine the embedding dimension of the Rossler system. The mutual information method, a widely used nonlinear dynamics analysis technique, calculates information content at given time delays to establish optimal embedding parameters. This typically involves computing the mutual information function I(τ) between the original time series and its delayed version, where the first minimum of this function indicates the optimal time delay. Cao's method, another established approach, determines the minimum embedding dimension required for proper phase space reconstruction of chaotic systems by analyzing the ratio E1(d) of false nearest neighbors as dimension increases. The algorithm implementation involves incrementally increasing the embedding dimension d and examining when E1(d) saturates, indicating sufficient dimension for system reconstruction. Our results demonstrate that this combined methodology enables more accurate analysis of Rossler system's dynamic characteristics, providing a foundation for future research in chaos control and chaos synchronization. The code implementation typically requires functions for mutual information calculation, phase space reconstruction, and nearest neighbor analysis using appropriate distance metrics.