Lyapunov Exponent Calculation with MATLAB Implementation

This document presents a MATLAB implementation for calculating Lyapunov exponents, which are fundamental mathematical measures for analyzing the dynamics of nonlinear systems. Lyapunov exponents quantify the exponential divergence or convergence of nearby trajectories in phase space, serving as a primary indicator for chaos detection in dynamical systems. The program implements numerical algorithms including the Wolf method or Benettin algorithm for computing the spectrum of Lyapunov exponents from time series data or system equations. The MATLAB code features a structured implementation with key functions handling phase space reconstruction, Jacobian matrix calculation, and orthogonalization procedures using QR decomposition. The program includes robust error handling and parameter validation for different system dimensions. Users can input custom differential equations or experimental data, with options for adjusting time steps, embedding dimensions, and normalization parameters. The implementation details the mathematical framework involving tangent space evolution and eigenvalue computation through repeated matrix operations. The code provides both maximal Lyapunov exponent calculation and full spectrum analysis, with visualization tools for tracking exponent convergence over time. This resource is particularly valuable for researchers and students in nonlinear dynamics, chaos theory, and complex system analysis, offering both educational insights and practical research tools for stability characterization and chaos quantification.