Explore MATLAB source code curated for "Lyapunov指数" with clean implementations, documentation, and examples.
This article provides comprehensive guidance on calculating Lyapunov exponents and constructing Poincaré sections for chaotic systems, including algorithm explanations and implementation approaches using numerical methods.
A MATLAB-based implementation for calculating Lyapunov exponents across diverse chaotic systems, featuring efficient algorithms and practical usability
Source code for predicting Lyapunov exponents: largest_lyapunov_exponent.m (calculates the largest Lyapunov exponent using Lü Jinhu's method), lyapunov_wolf.m (computes the largest Lyapunov exponent using Wolf's method), and G_P.m (implements G-P algorithm for correlation dimension calculation). Reference: "Improved Slope Displacement Prediction Algorithm Based on Lyapunov Exponents." These MATLAB implementations feature phase space reconstruction, nearest neighbor searching, and divergence rate computation for chaotic time series analysis.
Chaotic computing program source files—includes implementations of 5 different algorithms for calculating Lyapunov exponents: C-C algorithm, Minimum Data Volume algorithm, G-P algorithm, Correlation Dimension method, and Mutual Information method.
Implementation of a mixed programming approach for computing Lyapunov exponents with limited data
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.
MATLAB source code implementation for computing Lyapunov exponents with detailed algorithm explanation
A simple and effective alternative method for measure entropy - the approximate entropy approach. This method was applied to analyze the complexity of Logistic maps. Results demonstrate that Lyapunov exponents and measure entropy values show approximately linear relationships with complexity, while the functional relationship between fractal dimension and complexity remains difficult to determine, with unclear connections to Lyapunov exponents and measure entropy. The implementation involves calculating pattern repetitions in time series data with tolerance thresholds.
MATLAB program implementation for computing Lyapunov exponents using the small data method with detailed algorithm explanation and code structure analysis
This practical utility implements slope-based Lyapunov exponent calculation for time series analysis, widely used in nonlinear dynamics and time series processing with clear algorithmic implementation.