DYNAMICAL HYSTERESIS WITHOUT STATIC HYSTERESIS - SCALING LAWS AND ASYMPTOTIC EXPANSIONS

We study dynamical hysteresis in a simple class of nonlinear ordinary differential equations, namely first-order equations subject to sinuso idal forcing. The assumed nonlinearities are such that the area of the hysteresis loop vanishes as the forcing frequency tends to zero; in o ther words, there is no static hysteresis. Using regular and singular perturbation techniques, we derive the first term in the asymptotic ex pansion for the loop area as a function of the driving frequency, in t he limit of both large and small frequency. Although the theory was or iginally motivated by experiments on bistable semiconductor lasers, it is applied here to explain (and in some cases, to correct) the scalin g laws that were recently reported in numerical studies of mean-field kinetic Ising models of ferromagnets.