Structure analysis of the Lorenz-84 chaotic attractor

TL;DR

This paper investigates the complex structure of the Lorenz-84 chaotic attractor, revealing its organization around a period-2 cavity and introducing new visualization and analysis methods for weakly dissipative chaos.

Contribution

It introduces a color tracer mapping technique to analyze the Lorenz-84 attractor's structure and uncovers a new chaos-generating mechanism involving multidirectional stretching.

Findings

Attractor is organized around a period-2 cavity

Discovered a new chaos generation mechanism: multidirectional stretching

Validated structure representation using periodic orbits

Abstract

The structure of the Lorenz-84 attractor is investigated in this study. Its dynamics belonging to weakly dissipative chaos, classical approaches cannot be used to analyze its structure. The color tracer mapping is introduced for this purpose and used to extract the three-dimensional structure of the attractor. The analysis shows that the attractor is a non trivial case of toroidal chaos: it is organized around a period-2 cavity. Moreover, the structure reveals a new mechanism generating chaos in the attractor: a multidirectional stretching. The attractor structure is then artificially represented on a two-dimensional branched manifold and its validation performed using a set of periodic orbits previously extracted.