Dynamic approximation of rectangular loops and aftereffect

This paper presents a new approach to model hysteresis and aftereffect phenomena. A dynamic approximation of rectangular hysteresis loops is employed that leads to the representation of the input-output relationship as a first-order dynamical system driven by white noise. Closed-form expressions are derived for the output of rectangular loops in terms of convolution-type integrals. The formalism allows one to circumvent some of the mathematical challenges associated with history-dependent switching of rectangular hysteresis loops driven by stochastic processes.