Calculation of Lyapunov Exponent as a Chaos Detection Metric

This article explores chaotic phenomena and their quantitative detection metric - the Lyapunov exponent. The Lyapunov exponent serves as a fundamental method for quantifying the stability of chaotic systems, and we present a MATLAB implementation for its numerical computation. The subsequent sections will elaborate on the conceptual foundation of Lyapunov exponents and their application in characterizing chaotic behavior. We will further investigate the algorithmic approach for calculating Lyapunov exponents in MATLAB, including key implementation aspects such as phase space reconstruction using time-delay embedding, Jacobian matrix estimation for local linearization, and orthogonalization procedures to maintain numerical stability during exponent convergence. The discussion will extend to practical applications of the code for analyzing real-world chaotic systems, demonstrating how to initialize system parameters, handle time-series data preprocessing, and interpret the resulting exponent spectrum. Through this comprehensive guide, you will gain deeper insights into chaotic dynamics and develop proficiency in employing Lyapunov exponents as robust stability indicators for nonlinear systems.