A Delay-Duhem model for jump-resonance hysteresis

In this paper we present a Duhem hysteretic model that models jump resonance hysteresis in Dufflng´s oscillator. In order to obtain the Duhem model, we use a nonlinear oscillator that can output a harmonic signal of specified frequency and amplitude. We also use a sliding time averaging system that captures the mean square value of a variable-period signal. The presented Duhem model represents the excitation frequency versus response amplitude hysteresis of Dufflng´s oscillator in the sense of a persistent input-output loop under asymptotically slow periodic excitation. We also show that the jump resonance hysteresis is rate dependent.