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The theory of KM2O-Langevin equations and its applications to data analysis (III): Deterministic analysis

Published online by Cambridge University Press:  22 January 2016

Yasunori Okabe  and
Toshiyuki Yamane
Yasunori Okabe
Affiliation:
Department of Mathematical Engineering and Information Physics, Graduate School and Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
Toshiyuki Yamane
Affiliation:
Department of Mathematical Engineering and Information Physics, Graduate School and Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
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Abstract.

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A technique is given for detecting deterministic dynamics in time series. Some stochastic difference equations, called KM2O-Langevin equations, are extracted directly from given data. We can find deterministic dynamics in time series by evaluating the magnitude of innovation part of the KM2O-Langevin equations. We can further find chaotic dynamics in time series by predicting it from the viewpoint of the theory of KM2O-Langevin equations.

We apply our method to the data of measles and chicken pox, which are also treated by G. Sugihara and R.M. May in [1]. The result of numerical experiments indicates that there seem to exist some deterministic dynamics in both time series. It also suggests, however, that the data of measles seems to be chaotic while that of chicken pox not, which corresponds to the result of G. Sugihara and R.M. May.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 152 , December 1998 , pp. 175 - 201
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

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