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


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
Pages (from-to)6-15
Number of pages10
Publication statusPublished - 2015


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


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