Analysis of the semilinear Duhem model for rate-independent hysteresis

In this paper we consider a generalized Duhem model for hysteresis and provide a sufficient condition for the existence of hysteresis in the input-output map. Hysteresis is defined to be persistent phase shift at arbitrarily low frequency. The rate dependence of the hysteresis is also discussed, and we develop a rate-independent semilinear Duhem model with provable convergence properties. We also discuss the reversal behavior and orientation of the hysteretic map.