Modeling and Analysis of Duhem Hysteresis Operators With Butterfly Loops

In this work, we study and analyze a class of Duhem hysteresis operators that can exhibit butterfly loops. We study first the consistency property of such operator, which corresponds to the existence of an attractive periodic solution when the operator is subject to a periodic input signal. Subsequently, we study the two defining functions of the Duhem operator such that the corresponding periodic solutions can admit a butterfly input-output phase plot. We present a number of examples where the Duhem butterfly hysteresis operators are constructed using two zero-level set curves that satisfy some mild conditions.

Automated summary

In this work, we studied a class of Duhem hysteresis operators that can exhibit butterfly loops. We first investigated the consistency property of such operators, which corresponds to the existence of an attractive periodic solution under a periodic input signal. We then studied the two defining functions of the Duhem operator to allow corresponding periodic solutions to have a butterfly input-output phase plot. Several examples were presented where Duhem butterfly hysteresis operators were constructed using two zero-level set curves that satisfy certain mild conditions.