Computation of the largest Lyapunov exponent using recursive estimation with variable factor

TL;DR

This paper proposes a recursive method with variable data weighting to compute the largest Lyapunov exponent more accurately by accounting for error accumulation, showing improved results in most tested systems.

Contribution

It introduces a novel recursive estimation technique with variable data weighting for calculating the LLE, addressing error accumulation issues in previous methods.

Findings

More accurate LLE results in three of five systems tested.

Increased variance observed in two systems.

Method accounts for error accumulation over data processing.

Abstract

Chaotic systems have been investigated in the most diverse areas. One of the first steps in chaotic system research is the detection of chaos. The largest Lyapunov exponent (LLE) is one of the most widely used techniques for this purpose. Recently, techniques for calculating LLE have been developed taking into account the error due to the finite precision of computers. Recursive methods were employed to improve such algorithms. However, this method uniformly weighed the data used to calculate the LLE. This paper investigates the different weighing of the data based on the hypothesis that the initial data have a higher precision than the last data processed by the algorithm, since the process is subject to error accumulation. In five tested systems, the proposed method obtained more accurate results in three. However, there was an increase in the variance of the result obtained for two of the evaluated systems.