Prediction of flow dynamics using point processes

Yoshito Hirata, Thomas Stemler, Deniz Eroglu, Norbert Marwan

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

    Original languageEnglish
    Article number011101
    JournalChaos
    Volume28
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2018

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