Chaotic mechanism description by an elementary mixer for the template of an attractor

TL;DR

This paper introduces a framework using elementary mixers and linking matrices to uniquely describe the chaotic mechanisms and dynamics of attractors, addressing variability due to Poincaré section choices.

Contribution

It proposes a novel framework with elementary mixers and concatenation to classify chaotic mechanisms by size, providing a unique topological description.

Findings

Elementary mixers offer a consistent way to describe chaotic mechanisms.

Concatenation of mixers enables classification by size.

Framework reduces dependence on Poincaré section choice.

Abstract

A template describes the topological properties of a chaotic attractor. For attractors bounded by genus-1 torus, a linking matrix describes the topology of the template. It has been shown that the template depends on the Poincar\'e section chosen to perform the topological characterisation: four linking matrices describe four templates of the same chaotic attractor. The purpose of this article is to present a framework providing the elementary mixer of a template to have a unique way to describe chaotic mechanism and dynamics of a chaotic attractor. In this framework, chaotic mechanisms are represented by elementary mixers defined by elementary linking matrix. Using concatenation between mixers, a classification of chaotic mechanisms is proposed to categorise them by their size.