Analytical description of Recurrence Plots of white noise and chaotic processes

Abstract

We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling regions in the distribution of diagonals for oscillatory chaotic systems that are hinged to two prediction horizons and to the geometry of the attractor. These scaling regions cannot be observed with the Grassberger-Procaccia algorithm. Finally, we propose methods to estimate dynamical invariants from RPs.