On a topological criterion to select a recurrence threshold

Ioannis Andreadis; Athanasios D Fragkou; Theodoros E Karakasidis

doi:10.1063/1.5116766

On a topological criterion to select a recurrence threshold

Chaos. 2020 Jan;30(1):013124. doi: 10.1063/1.5116766.

Authors

Ioannis Andreadis¹, Athanasios D Fragkou², Theodoros E Karakasidis²

Affiliations

¹ International School of The Hague, Wijndaelerduin 1, 2554 BX The Hague, The Netherlands.
² Laboratory of Hydromechanics and Environmental Engineering, Department of Civil Engineering, University of Thessaly, 38344 Volos, Greece.

PMID: 32013497
DOI: 10.1063/1.5116766

Abstract

In this work, a topological criterion is proposed for selecting a recurrence threshold for constructing a recurrence plot of a time series. It is based on a metric structure of the set of the recurrence plots that is defined by the recurrence plot deviation distance among recurrence plots, introduced in a previous paper by the authors. In this process for a range of threshold values, the corresponding recurrence plots are constructed. Then, a value of the threshold is considered to be optimal when the image of its recurrence plot remains close to images of the other recurrence plots constructed for close values of thresholds based on the topological criterion introduced in the present work. The results are applied both to time series emanating from the Lorenz dynamical system and to Molecular Dynamic simulations.