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.
- Hidden attractor
- Power electronic converter
- Relay control system
Zhusubaliyev, Z. T., Mosekilde, E., Rubanov, V. G., & Nabokov, R. A. (2015). Multistability and hidden attractors in a relay system with hysteresis. Physica D: Nonlinear Phenomena, 306, 6-15. https://doi.org/10.1016/j.physd.2015.05.005