Multistability and hidden attractors in a relay system with hysteresis

Zhanybai T. Zhusubaliyev, Erik Mosekilde, Vasily G. Rubanov, Roman A. Nabokov

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations. (C) 2015 Elsevier B.V. All rights reserved.
Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
Volume306
Pages (from-to)6-15
Number of pages10
ISSN0167-2789
DOIs
Publication statusPublished - 2015

Keywords

  • Multistability
  • Hidden attractor
  • Power electronic converter
  • Relay control system
  • Hysteresis

Cite this

Zhusubaliyev, Zhanybai T. ; Mosekilde, Erik ; Rubanov, Vasily G. ; Nabokov, Roman A. / Multistability and hidden attractors in a relay system with hysteresis. In: Physica D: Nonlinear Phenomena. 2015 ; Vol. 306. pp. 6-15.
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Multistability and hidden attractors in a relay system with hysteresis. / Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.; Nabokov, Roman A.

In: Physica D: Nonlinear Phenomena, Vol. 306, 2015, p. 6-15.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Multistability and hidden attractors in a relay system with hysteresis

AU - Zhusubaliyev, Zhanybai T.

AU - Mosekilde, Erik

AU - Rubanov, Vasily G.

AU - Nabokov, Roman A.

PY - 2015

Y1 - 2015

N2 - For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations. (C) 2015 Elsevier B.V. All rights reserved.

AB - For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations. (C) 2015 Elsevier B.V. All rights reserved.

KW - Multistability

KW - Hidden attractor

KW - Power electronic converter

KW - Relay control system

KW - Hysteresis

U2 - 10.1016/j.physd.2015.05.005

DO - 10.1016/j.physd.2015.05.005

M3 - Journal article

VL - 306

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EP - 15

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -