The purpose of this study was to use topological methods of analysis to determine if a phase singularity exists for the neural respiratory oscillator. We studied resetting behavior of central respiratory rhythm, measured as phrenic nerve activity, by using brief stimulations of the superior laryngeal nerve in anesthetized paralyzed adult cats. The strength and timing of stimuli were varied, and the times of onset of subsequent breaths were measured. Two distinct types of phase resetting were identified: type 1 resetting for weak stimuli and type 0 resetting for strong stimuli. With stimuli of intermediate strength, we obtained a series of phase-resetting curves that defined a helicoid-resetting surface having a phase singularity near the transition between late expiration and early inspiration. In this domain resumption of breathing occurred at highly variable resetting times. The mammalian respiratory oscillator thus has qualitative characteristics of response to brief stimuli that are similar to those of other biological oscillators.