Time structure of chaotic attractors: A graphical view

1 July 1997

journal article
research article
Published by American Physical Society (APS) in Physical Review E

Vol. 56 (1) , 1188-1196
https://doi.org/10.1103/physreve.56.1188

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.

Keywords

This publication has 25 references indexed in Scilit:

NONLINEAR TIME SEQUENCE ANALYSIS
International Journal of Bifurcation and Chaos, 1991
State space reconstruction in the presence of noise
Physica D: Nonlinear Phenomena, 1991
Evidence for slow brain waves: a dynamical approach
Electroencephalography and Clinical Neurophysiology, 1991
Optimal Embeddings of Chaotic Attractors from Topological Considerations
Europhysics Letters, 1991
Time series analysis for system identification and diagnostics
Physica D: Nonlinear Phenomena, 1991
Statistical precision of dimension estimators
Physical Review A, 1990
The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1990
Noise reduction in dynamical systems
Physical Review A, 1988
Unstable periodic orbits and the dimensions of multifractal chaotic attractors
Physical Review A, 1988
Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in High Dimensional Chaotic Systems
Progress of Theoretical Physics, 1987