Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 720190, 31 pages
Review Article

Chaotic Time Series Analysis

Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200062, China

Received 25 December 2009; Accepted 7 February 2010

Academic Editor: Ming Li

Copyright © 2010 Zonghua Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Chaotic dynamical systems are ubiquitous in nature and most of them does not have an explicit dynamical equation and can be only understood through the available time series. We here briefly review the basic concepts of time series and its analytic tools, such as dimension, Lyapunov exponent, Hilbert transform, and attractor reconstruction. Then we discuss its applications in a few fields such as the construction of differential equations, identification of synchronization and coupling direction, coherence resonance, and traffic data analysis in Internet.