Detection of chaotic behavior in time series

TL;DR

This paper reviews methods for detecting chaos in time series, emphasizing the importance of distinguishing deterministic chaos from stochastic randomness, and demonstrates their application on classic chaotic systems.

Contribution

It compares standard and machine learning techniques for chaos detection and evaluates their effectiveness on well-known chaotic maps.

Findings

Machine learning methods can effectively identify chaos in time series.

Standard methods show reliable performance on classic chaotic systems.

The approach helps differentiate chaos from stochastic behavior.

Abstract

Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there originating time series. Chaos in time series resembles stochastic behavior, but apart of randomness it is totally deterministic and therefore chaotic data can provide us useful information. Therefore it is essential to have methods, which are able to detect chaos in time series, moreover to distinguish chaotic data from stochastic one. Here we present and discuss the performance of standard and machine learning methods for chaos detection and its implementation on two well known simple chaotic discrete dynamical systems - Logistic map and Tent map, which fit to the most of the definitions of chaos.