The Preisach model of hysteresis: fundamentals and applications

The Preisach model is a well-known model of hysteresis in the modern nonlinear science. This paper provides an overview of works that are focusing on the study of dynamical systems from various areas (physics, economics, biology), where the Preisach model plays a key role in the formalization of hysteresis dependencies. Here we describe the input-output relations of the classical Preisach operator, its basic properties, methods of constructing the output using the demagnetization function formalism, a generalization of the classical Preisach operator for the case of vector input-output relations. Various generalizations of the model are described here in relation to systems containing ferromagnetic and ferroelectric materials. The main attention we pay to experimental works, where the Preisach model has been used for analytic description of the experimentally observed results. Also, we describe a wide range of the technical applications of the Preisach model in such fields as energy storage devices, systems under piezoelectric effect, models of systems with long-term memory. The properties of the Preisach operator in terms of reaction to stochastic external impacts are described and a generalization of the model for the case of the stochastic threshold numbers of its elementary components is given.