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The appropriate selection of recurrence thresholds is a key problem inapplications of recurrence quantification analysis and related methods acrossdisciplines. Here, we discuss the distribution of pairwise distances betweenstate vectors in the studied system's state space reconstructed by means oftime-delay embedding as the key characteristic that should guide thecorresponding choice for obtaining an adequate resolution of a recurrence plot.Specifically, we present an empirical description of the distance distribution,focusing on characteristic changes of its shape with increasing embeddingdimension. Our results suggest that selecting the recurrence thresholdaccording to a fixed percentile of this distribution reduces the dependence ofrecurrence characteristics on the embedding dimension in comparison with othercommonly used threshold selection methods. Numerical investigations on someparadigmatic model systems with time-dependent parameters support theseempirical findings.

Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions