Border collisions inside the stability domain of a fixed point

Viktor Avrutin, Zhanybai T. Zhusubaliyev, Erik Mosekilde

Research output: Contribution to journalJournal articleResearchpeer-review

2 Downloads (Pure)

Abstract

Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.
Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
Volume321-322
Pages (from-to)1-15
Number of pages15
ISSN0167-2789
DOIs
Publication statusPublished - 2016

Keywords

  • Border-collision bifurcation
  • Piecewise-smooth map
  • Power electronic inverter

Cite this

Avrutin, Viktor ; Zhusubaliyev, Zhanybai T. ; Mosekilde, Erik. / Border collisions inside the stability domain of a fixed point. In: Physica D: Nonlinear Phenomena. 2016 ; Vol. 321-322. pp. 1-15.
@article{ff4c7a69dfc74f50abd4a12ddb62e5df,
title = "Border collisions inside the stability domain of a fixed point",
abstract = "Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.",
keywords = "Border-collision bifurcation, Piecewise-smooth map, Power electronic inverter",
author = "Viktor Avrutin and Zhusubaliyev, {Zhanybai T.} and Erik Mosekilde",
year = "2016",
doi = "10.1016/j.physd.2016.02.011",
language = "English",
volume = "321-322",
pages = "1--15",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",

}

Border collisions inside the stability domain of a fixed point. / Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik.

In: Physica D: Nonlinear Phenomena, Vol. 321-322, 2016, p. 1-15.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Border collisions inside the stability domain of a fixed point

AU - Avrutin, Viktor

AU - Zhusubaliyev, Zhanybai T.

AU - Mosekilde, Erik

PY - 2016

Y1 - 2016

N2 - Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.

AB - Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.

KW - Border-collision bifurcation

KW - Piecewise-smooth map

KW - Power electronic inverter

U2 - 10.1016/j.physd.2016.02.011

DO - 10.1016/j.physd.2016.02.011

M3 - Journal article

VL - 321-322

SP - 1

EP - 15

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -