  The effects of noise on the dynamics of nonlinear systems is known to lead to
many counter-intuitive behaviors. Using simple planar limit cycle oscillators,
we show that the addition of moderate noise leads to qualitatively different
dynamics. In particular, the system can appear bistable, rotate in the opposite
direction of the deterministic limit cycle, or cease oscillating altogether.
Utilizing standard techniques from stochastic calculus and recently developed
stochastic phase reduction methods, we elucidate the mechanisms underlying the
different dynamics and verify our analysis with the use of numerical
simulations. Lastly, we show that similar bistable behavior is found when
moderate noise is applied to the more biologically realistic FitzHugh-Nagumo
model.
