Why are some hysteresis loops shaped like a butterfly?

• Published in: 2009 American Control Conference pp. 3977 - 3982
• Main Authors: Drincic, B., Bernstein, D.S.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2009
• Subjects: Aerodynamics; Biological materials; Biological systems; Couplings; Ferroelectric materials; Frequency; Hysteresis; Nonlinear systems; Shape control; Steady-state
• DOI: 10.1109/ACC.2009.5159959
• ISBN: 142444523X; 9781424445233
• ISSN: 0743-1619

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.