Calculating Maximum Lyapunov Exponent from Time Series Using Small Data Quantities Method
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Resource Overview
This MATLAB program computes the maximum Lyapunov exponent from time series data using the small data quantities method with trajectory-based distance calculations.
Detailed Documentation
This MATLAB program implements the small data quantities method to calculate the maximum Lyapunov exponent from time series data. The algorithm begins by generating trajectories using each data point as a starting position. For each trajectory, the program computes the distance between consecutive points to determine the local Lyapunov exponent. The implementation uses vectorized operations for efficient distance calculations and employs multiple iterations to obtain a statistically robust average Lyapunov exponent. A key feature of this method is its ability to work with relatively small datasets, making it computationally efficient while maintaining accuracy. The code includes proper normalization of distances and implements exponential growth rate calculations through linear regression on the logarithmic distance evolution.
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