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

Authors:
Daolin Xu;Zhigang Li;Steven R. Bishop;Ugo Galvanetto
Affiliations:
Department of Engineering Mechanics, School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore;Department of Engineering Mechanics, School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore;Centre for Nonlinear Dynamics and its Applications, University College London, Gower Street, London WC1 6BT, UK;Department of Aeronautics, Imperial College of Science, Technology and Medicine, Prince Consort Road London SW7 2BY, UK
Venue:
Pattern Recognition Letters
Year:
2002

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Abstract

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.