Mathematical models of hysteresis

A new approach to the scalar Preisach model of hysteresis, which emphasizes its phenomenological nature and mathematical generality, is described. The theorem, which gives the necessary and sufficient conditions for the representation of actual hysteresis nonlinearities by the scalar Preisach model, is reported. The significance of this theorem is that it establishes the limits of applicability of Preisach´s model regardless of the physical nature of hysteresis. Then, the vector Preisach models are formulated and some basic properties of these models are briefly summarized. Numerical implementations of Preisach´s models are discussed and some computational results are given.