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

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...