Border effect corrections for diagonal line based recurrence quantification analysis measures

TL;DR

This paper investigates border effects and line thickening in recurrence plots, proposing correction schemes to improve the accuracy of diagonal line entropy measures for distinguishing regular and chaotic dynamics, even under noise.

Contribution

It introduces and systematically compares correction methods for border effects and line thickening in recurrence plots, enhancing the reliability of RQA measures in practical applications.

Findings

Corrections yield entropy values consistent with system dynamics.

Methods distinguish regular from chaotic motion effectively.

Corrections remain robust under noisy conditions.

Abstract

Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.