On a topological criterion to select a recurrence threshold

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.