A single-degree-of-freedom dynamic cutting fixture is used to map out a part of the lobed stability boundary in a simple high-speed machining experiment. The experiment reveals the hysteretic nature of the instability. A 1 DOF mechanical model is derived using parameters identified from the experiment. We then show the existence of a subcritical Hopf bifurcation in this delay-differential equation model which corresponds to the observed experimental instability. The calculation is based on center manifold reduction. Then time domain simulation is used to solve the full nonlinear equation of motion that allows for the tool to leave the workpiece giving excellent agreement with the experiment.