Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

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    Abstract

    © 2015 AIP Publishing LLC. We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.
    Original languageEnglish
    Article number12
    Pages (from-to)053101
    JournalChaos
    Volume25
    Issue number5
    DOIs
    Publication statusPublished - May 2015

    Fingerprint

    dynamical systems
    Time series
    partitions
    Dynamical systems
    Dynamical system
    Partition
    embedding
    time lag
    Chaotic Time Series
    Largest Lyapunov Exponent
    Time Lag
    Path Length
    Vertex of a graph
    Resonator
    Dynamical Behavior
    Network Structure
    Diode
    System Dynamics
    Shortest path
    Markov chains

    Cite this

    @article{ca429b46e5664850a8026f01361f37b7,
    title = "Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems",
    abstract = "{\circledC} 2015 AIP Publishing LLC. We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the R{\"o}ssler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.",
    author = "M. Mccullough and Michael Small and Thomas Stemler and Iu, {Ho Ching}",
    year = "2015",
    month = "5",
    doi = "10.1063/1.4919075",
    language = "English",
    volume = "25",
    pages = "053101",
    journal = "Chaos",
    issn = "1054-1500",
    publisher = "ACOUSTICAL SOC AMER AMER INST PHYSICS",
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    Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems. / Mccullough, M.; Small, Michael; Stemler, Thomas; Iu, Ho Ching.

    In: Chaos, Vol. 25, No. 5, 12, 05.2015, p. 053101.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

    AU - Mccullough, M.

    AU - Small, Michael

    AU - Stemler, Thomas

    AU - Iu, Ho Ching

    PY - 2015/5

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    AB - © 2015 AIP Publishing LLC. We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.

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