A bottom-up approach for recurrence detection based on sampling distance

Abstract

One of the major problems faced in the recurrence analysis of dynamical systems is the tangential motion effect affecting the structures in recurrence plots and their quantification. This issue roots to the choice of a threshold for recurrence, making it a crucial parameter for such analyses. It has been shown that a variable threshold following the dynamical changes of the system is more suited to the analysis of non-stationary data as it mitigates this effect. We study here the use of the distance separating successive points in the phase space as a reference for the recurrence threshold. The method relies on a single parameter while qualitatively and quantitatively providing stable recurrence structures as the previously suggested threshold based on the local maximum pairwise distance. This complete bottom-up approach is shown to be beneficial in the presence of abrupt transitions. It is also fairly noise-resistant and is not dependent on the sampling frequency in its normalized formulation. Furthermore, the sampling distance provides a clear reference for the occurrence of the tangential motion effect, allowing to define a default value for the threshold parameter to avoid it.