The Visual Boundary Recurrence Plot: A Closer Look into the Dynamics of Recurrence Plots

Abstract

In this paper, we introduce a new graphical tool, the visual boundary recurrence plot, in order to provide a more detailed visualization of the well-established method of recurrence plots. In this approach, we are coloring each point of the recurrence plot depending on whether the neighboring points in the vertical and horizontal directions are recurrent or not. We use this plot to study the stability of the textures of the recurrence plots viewing them as geometrical shapes under horizontal and vertical changes. In order to compare two recurrence plots, we define the visual boundary recurrence plot rate distance between their visual boundary recurrence plots to study their closeness/similarity. Finally, we introduce a topological criterion to select an optimal threshold for constructing a recurrence plot. A threshold is optimal when the recurrence plot associated with it remains similar to the ones that are constructed for consecutive values of backwards and forwards thresholds. The results are applied to recurrence plots of time series emanating from different sources: molecular dynamics simulations, Lorenz dynamical system, random noise and daily water level measurements of a river.