Time structure of chaotic attractors: A graphical view

Abstract

We present a simple and computationally inexpensive graphical method that unveils subtle correlations between short sequences of a chaotic time series. Similar events, even from noisy and nonstationary data, are clustered together and appear as well-defined patterns on a two-dimensional diagram and can be quantified. The general method is applied to the electrocardiogram of a patient with a malfunctioning pacemaker, the residence times of trajectories in the Lorenz attractor as well as the logistic map. In each case the diagrams unveil different aspects of the system's dynamics.