Unbiased recurrence plot quantification of chaotic dynamic systems by eliminating sojourn points

Abstract

Recurrence plots are nonlinear tools used to visualize the behavior of trajectories of Dynamic Systems. Occurrence of false points known as ‘sojourn points’ have biased recurrence plots. To solve this contentious issue, the use of high embedding dimension was proposed. However it required a lot of computation and was based on the phase space. For that, we proposed in this paper to compare four quantification techniques, by dropping out sojourn points from the recurrence test of time series. Firstly, a recurrence plot and embedding of two were used as reference methods. Secondly, the number of points in the pattern used for testing recurrences was increased and a m-pattern recurrence plot was introduced. Thirdly, a single system's output and its corresponding derivative were proposed. Numerical inference showed that it was sufficient to work on a single measurement regardless of the degrees of freedom of the considered system and thus the embedding dimension. The proposed techniques succeeded in eliminating sojourn points. They provided a tool for a clean unbiased recurrence plots which permits better analysis of chaotic dynamic systems.