Homoclinic orbit and hidden attractor in the Lorenz-like system describing the fluid convection motion in the rotating cavity

TL;DR

This paper investigates a Lorenz-like system modeling rotating fluid convection, revealing the existence of homoclinic orbits, chaotic attractors, and hidden attractors, with analytical and numerical localization methods demonstrated.

Contribution

It introduces the first localization of a hidden attractor in a Lorenz-like system describing fluid convection.

Findings

Existence of homoclinic trajectory in the system

Presence of a chaotic self-excited attractor

Localization of a hidden attractor

Abstract

In this paper a Lorenz-like system, describing the process of rotating fluid convection, is considered. The present work demonstrates numerically that this system, also like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for considered system, unlike the classical Lorenz one, along with self-excited attractor a hidden attractor can be localized. Analytical-numerical localization of hidden attractor is presented.