Calculating Delay Time t Using Mutual Information in Chaos Analysis
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This documentation presents a MATLAB implementation for mutual information computation in chaos analysis, with specific focus on determining the optimal delay time parameter t. The implementation begins by discretizing the time series into distinct states using histogram-based binning methods. Mutual information is then calculated between the original time series and its time-delayed version using probability distribution functions. The core algorithm iterates through different delay time values to identify the optimal t where mutual information reaches its first minimum - indicating sufficient independence between delayed coordinates. Key MATLAB functions utilized include histcounts for state discretization, unique for state identification, and custom mutual information calculation routines. The implementation leverages vectorization techniques for efficient computation and includes visualization components for analyzing mutual information versus delay time plots.
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