Modeling and analysis of Duhem hysteresis operators with butterfly loops

TL;DR

This paper investigates a class of Duhem hysteresis operators capable of exhibiting butterfly loops, analyzing their properties, conditions for periodic solutions, and constructing examples with specific phase plot behaviors.

Contribution

It introduces a detailed analysis of Duhem hysteresis operators with butterfly loops, including conditions for periodic solutions and methods for constructing such operators.

Findings

Existence of attractive periodic solutions under periodic inputs.

Conditions for butterfly input-output phase plots.

Construction of operators using zero-level set curves.

Abstract

In this work we study and analyze a class of Duhem hysteresis operators that can exhibit butterfly loops. We study firstly 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.