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Constructing ordinal partition transition networks from multivariate time series.

Jiayang Zhang1, Jie Zhou1, Ming Tang2

  • 1Department of Physics, East China Normal University, Shanghai, 200241, China.

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We introduce ordinal partition transition networks for analyzing multivariate time series, offering dynamic insights into complex systems. This method enhances traditional symbolic analysis for nonlinear dynamics.

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Area of Science:

  • Complex Systems Science
  • Nonlinear Dynamics
  • Data Analysis

Background:

  • Traditional methods often focus on scalar time series, limiting analysis of multivariate phenomena.
  • Empirical sciences frequently deal with multivariate data, requiring advanced analytical tools.

Purpose of the Study:

  • To extend ordinal partition transition networks to multivariate time series analysis.
  • To provide dynamic insights into underlying systems by analyzing pattern transitions.
  • To develop a novel entropy measure for characterizing ordinal partition transition dynamics.

Main Methods:

  • Construction of weighted directed networks from multivariate time series.
  • Representation of pattern transition properties in velocity space.
  • Development of an entropy measure sensitive to local geometric changes in phase space.

Main Results:

  • Demonstration of capturing phase coherence to non-coherence transitions.
  • Characterization of pathways leading to phase synchronization.
  • Identification of dynamic insights complementary to traditional symbolic analysis.

Conclusions:

  • Ordinal partition transition networks offer a powerful new approach for nonlinear multivariate time series.
  • The method provides dynamic insights and complements existing symbolic analysis techniques.
  • This approach is valuable for understanding complex system dynamics and transitions.