Calculating Lyapunov Exponents: Implementation and Algorithms

This document introduces predictive source code for calculating Lyapunov exponents and correlation dimensions. The primary MATLAB files include largest_lyapunov_exponent.m and G_P.m. The largest_lyapunov_exponent.m implementation utilizes Lü Jinhu's method to compute the largest Lyapunov exponent, employing phase space reconstruction and linear regression to quantify chaotic system sensitivity. Alternatively, lyapunov_wolf.m applies Wolf's method, which tracks the evolution of nearby trajectories in phase space to determine exponential divergence rates. The G_P.m file implements the Grassberger-Procaccia algorithm for correlation dimension calculation, using spatial correlation integrals to characterize system dimensionality. These algorithms enable slope displacement prediction through chaotic time series analysis, with Lyapunov exponents and correlation dimensions serving as key parameters for algorithm enhancement. Detailed explanations of these implementations can be found in the reference paper "Improved Slope Displacement Prediction Algorithm Based on Lyapunov Exponents." Each script includes modular functions for data preprocessing, embedding dimension optimization, and statistical validation of nonlinear dynamics parameters.