On a low-dimensional model for ferromagnetism

In this paper, we present a low-dimensional, energy-based model for ferromagnetic hysteresis. It is based on the postulates of Jiles and Atherton for modeling hysteresis losses. As a state space model, the system is a set of two state equations, with the time-derivative of the average applied magnetic field H˙ as the input, and the average magnetic field H and the average magnetization M as state variables. We show analytically that for a class of time-periodic inputs and initial condition at the origin, the solution trajectory converges to a periodic orbit. This models an observed experimental phenomenon.