Lyapunov Exponent Calculation Algorithm

This MATLAB program calculates Lyapunov exponents for analyzing chaotic behavior in dynamical systems. The implementation has undergone rigorous testing and is particularly suitable for MATLAB beginners exploring chaos theory. The core algorithm employs numerical differentiation techniques to quantify the exponential divergence rates of nearby trajectories in phase space - a fundamental characteristic of chaotic systems. Key functions include trajectory evolution using ODE solvers, Jacobian matrix calculations for linearized dynamics, and QR decomposition for orthogonalization to maintain numerical stability. Before executing the program, users should understand the theoretical background of Lyapunov exponents, particularly how they measure the stability and predictability of dynamical systems. The code demonstrates practical implementation of Wolf's algorithm for finite-time Lyapunov exponent calculation. For deeper technical understanding, consult MATLAB's documentation on differential equation solvers and review research papers on chaos theory. This program serves as an educational tool for better comprehending chaotic phenomena in nonlinear dynamical systems through hands-on computational experimentation.