Computing Lyapunov Exponents for Various Chaotic Systems

In my research, I utilized MATLAB programming to compute Lyapunov exponents for various complex chaotic systems. MATLAB proves to be an exceptionally powerful and user-friendly programming environment that enables rapid and accurate data analysis, leading to reliable conclusions. The implementation involves key numerical techniques such as the Benettin algorithm for tracking orthogonal divergence of nearby trajectories, Jacobian matrix calculations for linearized system dynamics, and QR decomposition for maintaining orthogonality during exponent estimation. Through MATLAB's computational capabilities, I gained deeper insights into chaotic system behaviors and discovered numerous fascinating phenomena. Specifically, the code employs ode45 solver for system integration, matrix normalization routines for stability, and progressive exponent averaging for convergence verification. Ultimately, MATLAB serves as an invaluable tool that empowers researchers to comprehensively understand complex dynamical systems through robust numerical implementation and visualization capabilities.