  Activated escape of a Brownian particle from the domain of attraction of a
stable focus over a limit cycle exhibits non-Kramers behavior: it is
non-Poissonian. When the attractor is moved closer to the boundary oscillations
can be discerned in the survival probability. We show that these oscillations
are due to complex-valued higher order eigenvalues of the Fokker-Planck
operator, which we compute explicitly in the limit of small noise. We also show
that in this limit the period of the oscillations is the winding number of the
activated stochastic process. These peak probability oscillations are not
related to stochastic resonance and should be detectable in planar dynamical
systems with the topology described here.
