  The Hopf oscillator has been shown to capture many phenomena of the auditory
and vestibular systems. These systems exhibit remarkable temporal resolution
and sensitivity to weak signals, as they are able to detect sounds that induce
motion in the sub-nanometer regime. In the present work, we find the analytic
response function of a nonisochronous Hopf oscillator to a step stimulus and
show that the system is most sensitive in the regime where noise induces
chaotic dynamics. We show that this regime also provides a faster response and
enhanced temporal resolution. Thus, the system can detect a very brief,
low-amplitude pulse. Finally, we subject the oscillator to periodic
delta-function forcing, mimicking a spike train, and find the exact analytic
expressions for the stroboscopic maps. Using these maps, we find a
period-doubling cascade to chaos with increasing force strength.
