A history-differential model for ferromagnetic hysteresis

A one-dimensional model of uniaxial magnetic hysteresis is proposed. Mainly, previous models investigated by Coleman and Hodgdon and Gentili and Giorgi are modified here in order to fit the behaviour of a wider class of ferromagnets. The properties fulfilled by the original models are preserved—for instance, the presence of the major loop, bounding all hysteresis paths, the existence and uniqueness of asymptotically stable periodic solutions (primitive loops), and the existence of a “universal” demagnetization process (a suitable alternating magnetic field, with slowly decreasing amplitude, reproducing the “virgin state”). Moreover, the equilibrium states turn out to be stable with respect to noises of small amplitude (static vibrostability) which is typical of permanent magnets.