Detecting chaos in a complex system

TL;DR

This paper evaluates chaos detection methods on high-dimensional systems, revealing challenges in identifying chaos in complex systems compared to simpler models like the Lorenz map.

Contribution

It demonstrates the limitations of standard chaos detection techniques when applied to high-dimensional, complex systems and explores how sampling step size affects chaos visibility.

Findings

Standard methods sometimes fail to detect chaos in 7D systems.

Sampling step size influences the ability to identify chaos.

Complex internal features may obscure chaos detection.

Abstract

The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number of parameters. The same diagnostic approaches have been applied to the 3D Lorenz map for comparison. The results show that for some of the sequences yielded from the 7D map, the adopted methods were not able to give as straightforward answer to the question if the system is chaotic as in the 3D case. Since the sequences, subject of the analysis, were not contaminated by noise and were sufficiently long, it could be assumed that such difficulties have arisen likely due to specific internal features of the more complex system. It was found also that an increase from 0.01 to 0.5 of the sampling step determining the sequences obtained from the 7D map, masks the chaos in some of them.