ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Сухарев Д. М., Koryakin V. A., Kazakov A. O. On Lorenz-type attractors in a six-dimensional generalization of the Lorenz model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 6, pp. 816-831. DOI: 10.18500/0869-6632-003133, EDN: LDKTZM

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Language: 
Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
517.925 + 517.93
DOI: 
10.18500/0869-6632-003133
EDN: 
LDKTZM

On Lorenz-type attractors in a six-dimensional generalization of the Lorenz model

Autors: 
Сухарев Дмитрий Михайлович, National Research University "Higher School of Economics"
Koryakin Vladislav Andreevich, National Research University "Higher School of Economics"
Kazakov Alexey Olegovich, National Research University "Higher School of Economics"
Abstract: 

The topic of the paper — Lorenz-type attractors in multidimensional systems. We consider a six-dimensional model that describes convection in a layer of liquid, taking into account impurities in the atmosphere and liquid, as well as the rotation of the Earth.

The main purpose of the work is to study bifurcations in the corresponding system and describe scenarios for the emergence of chaotic attractors of various types.

Results. It is shown that in the system under consideration, both a classical Lorenz attractor (the theory of which was developed in the works of Afraimovich–Bykov–Shilnikov) and an attractor of a new type, visually similar to the Lorenz attractor, but containing a symmetric pair of equilibrium states, can arise. It has been established that the Lorenz attractor in this system is born as a result of the classical scenario proposed by L. P. Shilnikov. We propose a new scenario for the emergence of an attractor of the second type via bifurcations inside the Lorenz attractor. In the paper we also discuss homoclinic and heteroclinic bifurcations that inevitably arise inside the found attractors, as well as their possible pseudohyperbolicity.
 

Key words: 
chaotic attractor
pseudohyperbolicity
Lorenz attractor
Lyapunov exponents
homoclinic bifurcations
heteroclinic bifurcations
Acknowledgments: 
The work was carried out with the financial support of the project “Mirror Laboratories” HSE University (Sections 1-3). The studies in Section 4 and Conclusion were financially supported by the Russian Science Foundation, grant No. 23-71-30008.
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Received: 
22.06.2024
Accepted: 
20.09.2024
Available online: 
14.11.2024
Published: 
29.11.2024
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