Calculating Lyapunov Exponents for Various Chaotic Systems

This document provides MATLAB source code for calculating Lyapunov exponents of various chaotic systems. Chaotic systems represent a class of dynamic systems exhibiting complex behaviors characterized by high uncertainty and sensitivity to initial conditions. Lyapunov exponents serve as crucial quantitative measures for describing system instability and predicting chaotic behavior patterns. The MATLAB implementation incorporates numerical algorithms such as the Wolf method for computing the largest Lyapunov exponent, and extended methods for calculating full Lyapunov spectra when required. Key functions include Jacobian matrix computation for linearized system dynamics, orthogonalization procedures using QR decomposition to maintain numerical stability, and time-series analysis techniques for experimental data. Researchers can utilize this program to explore chaotic system characteristics through parameter variation studies, bifurcation analysis, and long-term behavior prediction. The code supports customization for different chaotic systems including Lorenz, Rossler, and Henon maps by modifying system equations and corresponding Jacobian matrices. This enables deeper investigation into chaotic system properties, facilitating improved decision-making and forecasting capabilities in complex dynamic systems.