Stochastic aspects of hysteresis

A review of recent advances in the area of hysteretic nonlinearities driven by di.usion processes is presented. The analysis of these systems is based on the Preisach formalism for the description of hysteresis to represent complex nonlinearities as a weighted superposition of rectangular loops. The mathematical theory of di.usion processes on graphs is then applied to solve problems for stochastically driven hysteresis loops. Closed form expressions for the expected value and spectral density of the output are obtained, and sample computations for these quantities are presented. Because of the universality of the Preisach model, this approach can be used to investigate stochastic aspects in hysteretic systems of various physical origins.