  An ensemble of uncoupled limit-cycle oscillators receiving common Poisson
impulses shows a range of non-trivial behavior, from synchronization,
desynchronization, to clustering. The group behavior that arises in the
ensemble can be predicted from the phase response of a single oscillator to a
given impulsive perturbation. We present a theory based on phase reduction of a
jump stochastic process describing a Poisson-driven limit-cycle oscillator, and
verify the results through numerical simula- tions and electric circuit
experiments. We also give a geometrical interpretation of the synchronizing
mechanism, a perturbative expansion to the stationary phase distribution, and
the diffusion limit of our jump stochastic model.
