### Abstract

Original language | English |
---|---|

Article number | 12 |

Pages (from-to) | 053101 |

Journal | Chaos |

Volume | 25 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2015 |

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### Cite this

*Chaos*,

*25*(5), 053101. [12]. https://doi.org/10.1063/1.4919075

}

*Chaos*, vol. 25, no. 5, 12, pp. 053101. https://doi.org/10.1063/1.4919075

**Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems.** / Mccullough, M.; Small, Michael; Stemler, Thomas; Iu, Ho Ching.

Research output: Contribution to journal › Article

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

Y1 - 2015/5

N2 - © 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.

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.

U2 - 10.1063/1.4919075

DO - 10.1063/1.4919075

M3 - Article

VL - 25

SP - 053101

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 5

M1 - 12

ER -