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Avtomatika i Telemekhanika, 2020, Issue 8, Pages 29–39
DOI: https://doi.org/10.31857/S0005231020080036 (Mi at15561) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Topical issue

Bifurcations of chaotic attractors in a piecewise smooth Lorenz-type system

V. N. Belykhab, N. V. Barabashba, I. V. Belykhc

a Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, Russia
b Volga State University of Water Transport, Nizhny Novgorod, Russia
c Georgia State University, Atlanta, USA
Full-text PDF (691 kB) Citations (5)
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DOI: https://doi.org/10.31857/S0005231020080036
Abstract: We study the dynamics of a piecewise-smooth system of differential equations for which the existence of a strange Lorenz-type attractor had been rigorously proved previously and bifurcation mechanisms of its birth had been obtained. In this work we discuss the destruction of this attractor due to the appearance of sliding motions in its structure. Using qualitative and numerical methods, we study a complex sequence of attractor bifurcations that leaves in the system a globally stable limit cycle. We show that this sequence is based on $C$-bifurcations and bifurcations of multi-loop homoclinic trajectories.
Keywords: dynamic system, bifurcations, limit cycle, sliding motion, strange attractor, chaos.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00556_а
18-31-20052_Стабильность
National Science Foundation DMS-1909924
Russian Science Foundation 19-12-00367
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 0729-2020-0036, the Russian Science Foundation, project no. 19-12-00367 (numerics; to V.N.B. and N.V.B), and the US National Science Foundation, grant no. DMS-1909924 (to I.V.B.).
Presented by the member of Editorial Board: B. T. Polyak

Received: 23.07.2019
Revised: 18.10.2019
Accepted: 30.01.2020
English version:
Automation and Remote Control, 2020, Volume 81, Issue 8, Pages 1385–1393
DOI: https://doi.org/10.1134/S0005117920080020
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. N. Belykh, N. V. Barabash, I. V. Belykh, “Bifurcations of chaotic attractors in a piecewise smooth Lorenz-type system”, Avtomat. i Telemekh., 2020, no. 8, 29–39; Autom. Remote Control, 81:8 (2020), 1385–1393
Citation in format AMSBIB
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\pages 29--39
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