From quasiperiodicity to high-dimensional chaos without intermediate low-dimensional chaos

TL;DR

This paper investigates a direct transition to high-dimensional chaos in a system of three coupled Lorenz oscillators, revealing a heteroclinic explosion as the organizing mechanism without intermediate low-dimensional chaos.

Contribution

It provides a detailed geometric analysis of the route to high-dimensional chaos, identifying heteroclinic explosion as the key transition mechanism in coupled Lorenz oscillators.

Findings

Transition organized by heteroclinic explosion

Resembles classical homoclinic explosion in Lorenz model

No intermediate low-dimensional chaos observed

Abstract

We study and characterize a direct route to high-dimensional chaos (i.e. not implying an intermediate low-dimensional attractor) of a system composed out of three coupled Lorenz oscillators. A geometric analysis of this medium-dimensional dynamical system is carried out through a variety of numerical quantitative and qualitative techniques, that ultimately lead to the reconstruction of the route. The main finding is that the transition is organized by a heteroclinic explosion. The observed scenario resembles the classical route to chaos via homoclinic explosion of the Lorenz model.