Calculating Lyapunov Exponent from Time Series Using Slope Method

Resource Overview

This practical utility implements slope-based Lyapunov exponent calculation for time series analysis, widely used in nonlinear dynamics and time series processing with clear algorithmic implementation.

Detailed Documentation

In nonlinear dynamics and time series analysis, the slope method for calculating Lyapunov exponents is frequently employed. Determining Lyapunov exponents is crucial for investigating the dynamical properties of time series. The practical implementation typically involves algorithms that track the divergence rates of nearby trajectories in phase space reconstruction. Key computational steps include: phase space reconstruction using time-delay embedding, calculating the distances between neighboring points, monitoring exponential divergence through linear regression on logarithmic distance plots, and finally extracting Lyapunov exponents from the slope of the divergence curve. These compact computational tools enable efficient Lyapunov exponent estimation, making mastery of both the calculation methodology and its applications highly valuable for dynamical systems analysis.