 03375 Nils Berglund and Barbara Gentz
 On the noiseinduced passage through an unstable periodic orbit I:
Twolevel model
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Aug 18, 03

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Abstract. We consider the problem of stochastic exit from a planar domain, whose
boundary is an unstable periodic orbit, and which contains a stable
periodic orbit. This problem arises when investigating the distribution of
noiseinduced phase slips between synchronized oscillators, or when
studying stochastic resonance far from the adiabatic limit. We introduce a
simple, piecewise linear model equation, for which the distribution of
firstpassage times can be precisely computed. In particular, we obtain a
quantitative description of the phenomenon of cycling: The distribution of
firstpassage times rotates around the unstable orbit, periodically in the
logarithm of the noise intensity, and thus does not converge in the
zeronoise limit. We compute explicitly the cycling profile, which is
universal in the sense that in depends only on the product of the period of
the unstable orbit with its Lyapunov exponent.
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