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Refined nonuniform embedding for coupling detection in multivariate time series.

Ziyu Jia1,2,3, Youfang Lin1,2,3, Yunxiao Liu1,2,3

  • 1School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China.

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We developed a new information theory method for state-space reconstruction, improving complex system analysis. This approach enhances coupling detection in various systems and reveals delay propagation networks.

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Area of Science:

  • Complex Systems Analysis
  • Information Theory
  • Dynamical Systems

Background:

  • State-space reconstruction is crucial for understanding complex systems.
  • Existing methods struggle with high-dimensional conditional mutual information and optimal time delay selection.
  • Nonuniform reconstruction methods face challenges in accurately characterizing system dynamics.

Purpose of the Study:

  • To propose a novel nonuniform embedding method for state-space reconstruction based on information theory.
  • To address limitations in estimating conditional mutual information and selecting optimal time delays.
  • To enhance the characterization and coupling detection of multivariable complex systems.

Main Methods:

  • Framing nonuniform embedding within information theory.
  • Utilizing a low-dimensional approximation of conditional mutual information for time delay selection.
  • Employing particle swarm optimization to solve the time delay selection problem.

Main Results:

  • The proposed method yields embedded vectors with high independence and low redundancy.
  • Successfully characterizes multivariable complex systems and detects internal coupling.
  • Demonstrates robust performance in coupling detection across linear stochastic, nonlinear stochastic, and chaotic systems.
  • Identified the role of small airports in delay propagation networks through network construction.

Conclusions:

  • The developed nonuniform embedding method offers a powerful tool for state-space reconstruction.
  • It significantly improves the analysis of complex system dynamics and interactions.
  • The method has practical applications, as shown in the analysis of airport delay propagation.