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A practical method for estimating coupling functions in complex dynamical systems.

Isao T Tokuda1, Zoran Levnajic2, Kazuyoshi Ishimura1

  • 1Department of Mechanical Engineering, Ritsumeikan University, Kusatsu, Japan.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
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Summary
This summary is machine-generated.

This study reviews a method for reconstructing coupling functions and network topology from empirical data. The method is applied to various systems, demonstrating its broad applicability in network science.

Keywords:
coupling functionparameter estimationphase dynamics

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Area of Science:

  • Network Science
  • Dynamical Systems
  • Complex Systems

Background:

  • Reconstructing network topology and coupling equations from observed dynamics is a key challenge in network science.
  • Existing methods often require system interference or are limited in scope.
  • A previously developed method (Tokuda et al., 2007) can infer coupling functions and natural frequencies from time series data of limit-cycle oscillators.

Purpose of the Study:

  • To provide a comprehensive review of the Tokuda et al. (2007) method for a broader scientific audience.
  • To demonstrate the method's versatility through diverse applications.
  • To highlight the method's utility in network reconstruction and dynamical system analysis.

Main Methods:

  • Review and explanation of a method for inferring coupling functions and network topology from empirical time series data.
  • Application of the method to: network connectivity detection, phase sensitivity function inference, chaotic oscillator interaction approximation, and experimental data analysis.
  • Focus on methods applicable to real-world data without system interference.

Main Results:

  • The reviewed method successfully reconstructs coupling functions and network topology from empirical data.
  • Applications demonstrate the method's effectiveness in diverse scenarios, including chaotic systems and experimental circuits.
  • The method's range of applicability is reaffirmed and extended.

Conclusions:

  • The method offers a powerful tool for network reconstruction, applicable beyond physics.
  • It enables the inference of dynamical interactions from observational data.
  • The review makes this advanced technique accessible to a wider scientific community, fostering interdisciplinary research.