Why are some hysteresis loops shaped like a butterfly?

In this paper we investigate the origins of butterfly-shaped hysteresis maps. In particular, we show that there exist 2-to-1 maps that transform oriented simple closed curves into multi-loop closed curves with loops of opposite orientations. As an illustrative application, the hysteretic input-outpu...

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Bibliographic Details
Published in2009 American Control Conference pp. 3977 - 3982
Main Authors Drincic, B., Bernstein, D.S.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2009
Subjects
Aerodynamics
Biological materials
Biological systems
Couplings
Ferroelectric materials
Frequency
Hysteresis
Nonlinear systems
Shape control
Steady-state
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Summary:In this paper we investigate the origins of butterfly-shaped hysteresis maps. In particular, we show that there exist 2-to-1 maps that transform oriented simple closed curves into multi-loop closed curves with loops of opposite orientations. As an illustrative application, the hysteretic input-output map of the preloaded two-bar linkage mechanism becomes a butterfly when a 2-to-1 map is applied to it. In this case, the application of the 2-to-1 map to the hysteresis loop is equivalent to plotting an alternative output variable. We also investigate the hysteretic maps of ferroelectric materials that are transformed into a butterfly through a 2-to-1 map.
ISBN:142444523X
9781424445233
ISSN:0743-1619
2378-5861
DOI:10.1109/ACC.2009.5159959