The processes inside the arc tube of high-intensity discharge lamps are inves- tigated by finite element simulations. The behavior of the gas mixture inside the arc tube is governed by differential equations describing mass, energy and charge conservation as well as the Helmholtz equation for the acoustic pressure and the Navier-Stokes equation for the flow driven by the buoyancy and the acous- tic streaming force. The model is highly nonlinear and requires a recursion proce- dure to account for the impact of acoustic streaming on the temperature and other fields. The investigations reveal the presence of a hysteresis and the correspond- ing jump phenomenon, quite similar to a Duffing oscillator. The similarities and, in particular, the differences of the nonlinear behavior of the high-intensity dis- charge lamp to that of a Duffing oscillator are discussed. For large amplitudes the high-intensity discharge lamp exhibits a stiffening effect in contrast to the Duffing oscillator.