Journal article
Torus Birth Bifurcations in a DC/DC Converter
Considering a pulsewidth modulated dc/dc converter as an example, this paper describes a border-collision bifurcation that can lead to the appearance of quasi-periodicity in piecewise-smooth dynamical systems. We demonstrate how a two-dimensional torus can arise from a periodic orbit through a bifurcation in which two complex-conjugate Poincare characteristic multipliers jump abruptly from the inside to the outside of the unit circle.
The torus may be ergodic or resonant. However, in both cases the diameter of the torus develops approximately linearly with the distance to the bifurcation point as opposed to the characteristic parabolic form of the well-known Neimark-Sacker bifurcation. The paper also considers the birth of a torus via a subcritical Neimark-Sacker bifurcation in the piecewise-smooth system.
Particular emphasis is given to the development of resonance zones via border-collision bifurcations
| Language: | English |
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| Publisher: | IEEE |
| Year: | 2006 |
| Pages: | 1839-1850 |
| ISSN: | 15580806 and 15498328 |
| Types: | Journal article |
| DOI: | 10.1109/TCSI.2006.879060 |
Bifurcation Border-collision bifurcations DC-DC power converters DC-DC power convertors DC/DC converter Digital relays Electronic circuits Linear approximation Neimark-Sacker bifurcation Poincare characteristic multipliers jump Power system relaying Pulse circuits Pulse modulation Pulse width modulation converters Resonance bifurcation border-collision bifurcation multiplying circuits periodic orbit piecewise smooth system piecewise-smooth dynamical systems quasi-periodicity quasiperiodicity torus birth bifurcations
