Coherence properties of cycling chaos

•Coherence properties of cycling chaos are studied numerically.•Imperfectness leads to a coherent chaos, while instability results in a low coherent dynamics.•The properties are illustrated for Lorenz, Roessler, and logistic map models.

Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switchings 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.