Estimation of periodic-like motions of chaotic evolutions using detected unstable periodic patterns

We introduce an approach to detect cyclical patterns embedded within chaotic data and make use of the detected patterns to estimate periodic-like motions in a chaotic process. A chaotic attractor contains many unstable periodic orbits (UPOs). The UPOs are hidden cyclical patterns that dominate the dynamical evolution of the system. Knowledge of UPOs can be used for estimating the trends of chaotic evolutions. A numerical experiment is conducted to illustrate an application on the business cycle detection. (C) 2002 Elsevier Science; B.V. All rights reserved.