 96401 Robert S. Maier and Daniel L. Stein
 Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle
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Sep 7, 96

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Abstract. Suppose a twodimensional 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 analysing
the associated FokkerPlanck equation we show that in general, the
weaknoise escape rate is nonArrhenius: it includes a factor that is
periodic in the logarithm of the noise strength. The presence of this
slowly oscillating factor is due to the nonequilibrium potential of the
system being nondifferentiable at the limit cycle. We point out the
implications for the weaknoise limit of stochastic resonance models.
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