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Based on previous experimental and analytical studies, the nonsmooth dynamical model of a superconducting resonator is discussed. The device is a superconducting sensor whose key elements are a sensor probe attached to a conducting ring, around which flows an electric current. The ring is interrupted by a microbridge of a superconducting material, whose temperature can be altered to sensitively control the device’s conductivity. In certain conditions, novel self-sustaining power oscillations are observed, and can suddenly disappear. It was previously shown that this disappearance can be described by a periodic attractor undergoing a catastrophic sliding bifurcation. Here we reveal the sequence of bifurcations that leads up to this event, beginning with the change in stability of a fixed point that creates an attractor, and the birth of a saddle-type periodic orbit by means of a Hopf-like discontinuity-induced bifurcation.