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Estimates are derived for the mean recurrence time of orbits in the neighborhood of an attracting homoclinic orbit or heteroclinic cycle in an ordinary differential equation, subject to small additive random noise. The theory presented is illustrated with numerical simulations of several systems, including ones invariant under symmetry groups, for which such heteroclinic attractors are structurally stable. The physical implications of the work presented are briefly discussed.
Stone et al. (Fri,) studied this question.