A variable threshold for recurrence based on local attractor density

Abstract

Recurrence plots along with their quantification measures have demonstrated their usefulness for the study of dynamical systems in many fields. The distance threshold for recurrence is a crucial parameter influencing the observed recurrence structures, thus, the related quantification measures, and have been the object of several studies to find its optimal value. We suggest here a definition of recurrence based on the local attractor density to obtain more qualitative recurrence plots capturing the dynamics at different scales without suffering from variations in the tangential motion effect. The method is qualitatively and quantitatively compared with common thresholding methods on different signals. It is shown that the suggested recurrence plot has more uniform line structures and is less sensitive to the threshold parameter. We also present a modification enhancing its robustness to noise.