Rs. Maier et Dl. Stein, OSCILLATORY BEHAVIOR OF THE RATE OF ESCAPE THROUGH AN UNSTABLE LIMIT-CYCLE, Physical review letters, 77(24), 1996, pp. 4860-4863
Suppose a two-dimensional dynamical system has a stable attractor that
is surrounded by an unstable limit cycle. If the system is additively
perturbed by white noise, the rate of escape through the limit cycle
will fall off exponentially as the noise strength tends to zero. By an
alyzing the associated Fokker-Planck equation we show that in general
the weak-noise escape rate is non-Arrhenius: it includes a factor that
is periodic in the logarithm of the noise strength. The presence of t
his slowly oscillating factor is due to the nonequilibrium potential o
f the system being nondifferentiable at the limit cycle. We point out
the implications for the weak-noise limit of stochastic resonance mode
ls.