Calculation of Lyapunov Exponents - Classic MATLAB Implementation

This program offers a comprehensive MATLAB implementation for calculating Lyapunov exponents, which are crucial metrics for analyzing the stability and chaotic properties of dynamical systems. The code employs sophisticated numerical algorithms including QR decomposition for orthonormalization and time series analysis techniques to accurately compute the spectrum of Lyapunov exponents. Key features include efficient state space reconstruction, proper handling of tangent space dynamics, and implementation of the standard algorithm for exponent calculation. The program structure allows for easy modification of system parameters and integration methods, making it adaptable to various differential equations and discrete maps. Users can gain deeper insights into system behavior through the computed exponents, which quantify the average exponential divergence or convergence of nearby trajectories in phase space. The implementation includes error handling and validation checks to ensure reliable results for both autonomous and non-autonomous systems. This practical tool serves as an ideal solution for researchers and students working on nonlinear dynamics, chaos theory, and stability analysis, providing a solid foundation for further investigations into complex system behavior.