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JOURNALS // Avtomatika i Telemekhanika // Archive

Avtomat. i Telemekh., 2020 Issue 8, Pages 29–39 (Mi at15561)

This article is cited 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

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.

Presented by the member of Editorial Board: B. T. Polyak

Received: 23.07.2019
Revised: 18.10.2019
Accepted: 30.01.2020

DOI: 10.31857/S0005231020080036


 English version:
Automation and Remote Control, 2020, 81:8, 1385–1393

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© Steklov Math. Inst. of RAS, 2024