Border Collision Route to Quasiperiodicity: Numerical Investigation and Experimental Confirmation

Zhanybai Zhusubaliyev, Erik Mosekilde, S. Maity, S. Mohanan, S. Banerjee

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Abstract

Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewise-linear normal form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed curve, there may be transitions between an ergodic torus and a resonance torus, but the mechanism of creation for the resonance tongues is distinctly different from that observed in smooth maps. The transition from a stable focus point to a resonance torus may lead directly to a new focus of higher periodicity, e.g., a period-5 focus. This article also contains a discussion of torus destruction via a homoclinic bifurcation in the piecewise-linear normal map. Using a dc–dc converter with two-level control as an example, we report the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation. ©2006 American Institute of Physics
Original languageEnglish
JournalChaos
Volume16
Issue number2
Pages (from-to)023122
ISSN1054-1500
DOIs
Publication statusPublished - 2006

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Copyright (2006) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

Cite this

Zhusubaliyev, Z., Mosekilde, E., Maity, S., Mohanan, S., & Banerjee, S. (2006). Border Collision Route to Quasiperiodicity: Numerical Investigation and Experimental Confirmation. Chaos, 16(2), 023122. https://doi.org/10.1063/1.2208565