Since the MPEP in the models considered here spirals geometrically into the barrier, the point at which it gets within this distance will cycle around the limit cycle as the noise strength goes to 0, periodically in the logarithm of the noise strength. If the effective diffusivity varies with position along the limit cycle, one would then expect the escape rate to be periodically modulated. That is what we have shown to occur. We expect the phenomenon of slow oscillations is relevant to stochastic resonance in multistable continuous systems. Gang et al. have recently considered such systems, with the addition of time-periodic forcing and external noise.
Steady states are then periodic attractors, separated by unstable limit cycles.