2003/08/18 by Nils Berglund, Barbara Gentz · 1 citation
Biochemistry, Genetics and Molecular Biology · Environmental Science · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Ecosystem dynamics and resilience #math.PR #msc:34F05 #msc:37H20 #msc:60H10 #nlin.SI #stochastic dynamics and bifurcation
paper · pdf · doi:10.1023/b:joss.0000013966.54504.da
published as J. Statist. Phys. 114:1577-1618 (2004) · 32 pages, 7 figures
arxiv created 2003/08/18 · openalex publication_date 2004/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 noise-induced 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 first-passage times can be precisely computed. In particular, we obtain a quantitative description of the phenomenon of cycling: The distribution of first-passage times rotates around the unstable orbit, periodically in the logarithm of the noise intensity, and thus does not converge in the zero-noise 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.