  Cycling chaos is a heteroclinic connection between several chaotic
attractors, at which switching between the chaotic sets occur at growing time
intervals. Here we characterize the coherence properties of these switchings,
considering nearly periodic regimes that appear close to the cycling chaos due
to imperfections or to instability. Using numerical simulations of coupled
Lorenz, Roessler, and logistic map models, we show that the coherence is high
in the case of imperfection (so that asymptotically the cycling chaos is very
regular), while it is low close to instability of the cycling chaos.
