Estimating the Largest Lyapunov Exponent Based on Conditional Number

TL;DR

This paper introduces a novel method for calculating the largest Lyapunov exponent using the conditional number, demonstrating its effectiveness on four discrete maps to assess system chaos and stability.

Contribution

It proposes a new approach for Lyapunov exponent estimation based on the conditional number, enhancing accuracy in stability analysis.

Findings

Effective in estimating the largest Lyapunov exponent

Applicable to various discrete maps

Provides a reliable measure of system chaos

Abstract

The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed and developed for its calculation. The present work proposes a method for the calculation of the largest Lyapunov exponent, based on conditional number of the function, which describes the loss of bits in the simulation based on relative rounding error. Four discrete maps are used to show the effectiveness of the proposed method.