%0 Journal Article %1 ISI:000386991300001 %A Avrutin, Viktor %A Zhusubaliyev, Zhanybai T. %A Mosekilde, Erik %C PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS %D 2016 %I ELSEVIER SCIENCE BV %J PHYSICA D-NONLINEAR PHENOMENA %K Border-collision Piecewise-smooth bifurcation} electronic inverter; map; {Power %P 1-15 %R 10.1016/j.physd.2016.02.011 %T Border collisions inside the stability domain of a fixed point %V 321 %X 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. (C) 2016 Elsevier B.V. All rights reserved.

@article{ISI:000386991300001, 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. (C) 2016 Elsevier B.V. All rights reserved.}}, added-at = {2017-05-18T11:32:12.000+0200}, address = {{PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}}, affiliation = {{Avrutin, V (Reprint Author), Univ Stuttgart, Inst Syst Theory \& Automat Control, Pfaffenwaldring 9, D-70550 Stuttgart, Germany. Avrutin, Viktor, Univ Stuttgart, Inst Syst Theory \& Automat Control, Pfaffenwaldring 9, D-70550 Stuttgart, Germany. Zhusubaliyev, Zhanybai T., Southwest State Univ, Dept Comp Sci, 50 Years October Str,94, Kursk 305040, Russia. Mosekilde, Erik, Tech Univ Denmark, Dept Phys, Fysikvej 309, DK-2800 Lyngby, Denmark.}}, author = {Avrutin, Viktor and Zhusubaliyev, Zhanybai T. and Mosekilde, Erik}, author-email = {{Viktor.Avrurin@ist.uni-stuttgart.de Zhanybai@hotmail.com Erik.Mosekilde@fysik.dtu.dk}}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/27d979aa7a76f19e4e54f7b1a2c5444af/hermann}, doi = {{10.1016/j.physd.2016.02.011}}, eissn = {{1872-8022}}, funding-acknowledgement = {{German Research Foundation {[}AV 111/1-3]}}, funding-text = {{The work of V. Avrutin was partially supported by the German Research Foundation within the scope of the project ``Organizing centers in discontinuous dynamical systems: bifurcations of higher codimension in theory and applications{''}, AV 111/1-3.}}, interhash = {6700a091fdbee04fbff1cb08ffd36888}, intrahash = {7d979aa7a76f19e4e54f7b1a2c5444af}, issn = {{0167-2789}}, journal = {{PHYSICA D-NONLINEAR PHENOMENA}}, keywords = {Border-collision Piecewise-smooth bifurcation} electronic inverter; map; {Power}, keywords-plus = {{SYSTEMS}}, language = {{English}}, month = {{MAY 1}}, number-of-cited-references = {{16}}, orcid-numbers = {{Mosekilde, Erik/0000-0001-7575-8543}}, pages = {{1-15}}, publisher = {{ELSEVIER SCIENCE BV}}, research-areas = {{Mathematics; Physics}}, researcherid-numbers = {{Mosekilde, Erik/B-2030-2016}}, times-cited = {{0}}, timestamp = {2017-05-18T09:32:12.000+0200}, title = {{Border collisions inside the stability domain of a fixed point}}, type = {{Article}}, volume = {{321}}, web-of-science-categories = {{Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical}}, year = {{2016}} }