Study of a play-like operator

In this paper, we consider a play-like hysteresis operator defined by an nth order rate-independent differential system. We investigate the properties of the operator for n = 1 and 2. We show that the operator for n = 2 satisfies a one-step wiping out property. This result can be extended to show that the nth order operator satisfies an (n - 1)-th step wiping out property. Thus the new family of operators fall between the first-order differential equation models that do not satisfy any wiping-out properties and the Preisach-type operator that can show, in general, a countably infinite-step wiping out property. We will show that the "backlash-like" operator defined by Su, Stepanenko, Svoboda and Leung (SSSL) is a special case of our operator for n = 1.