Bifurcations of Chaotic Attractors in a Piecewise Smooth Lorenz-Type System

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 th...

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Bibliographic Details
Published inAutomation and remote control Vol. 81; no. 8; pp. 1385 - 1393
Main Authors Belykh, V.N., Barabash, N.V., Belykh, I.V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2020
Springer Nature B.V
Subjects
639/301/1034/1035
639/925/357/995
Attractors (mathematics)
Bifurcations
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Chaos theory
Computer-Aided Engineering (CAD
Control
Differential equations
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Numerical methods
Robotics
Systems Theory
Topical Issue
limit cycle
chaos
bifurcations
dynamic system
strange attractor
sliding motion
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Summary: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.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117920080020