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This study introduces two novel numerical methods to detect and analyze coupling in time series data. These methods effectively identify interdependence and directionality, even in complex nonlinear systems.

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Area of Science:

  • Nonlinear dynamics
  • Time series analysis
  • Complex systems

Background:

  • Understanding interactions within complex systems is crucial.
  • Existing methods for time series coupling analysis have limitations.
  • Deterministic nonlinear systems present unique challenges for coupling detection.

Purpose of the Study:

  • To propose novel numerical methods for detecting and analyzing coupling in time series.
  • To determine the directionality of coupling and identify latent coupling.
  • To provide practical tools for analyzing simultaneous system recordings.

Main Methods:

  • Development of two numerical methods based on order statistics.
  • Utilizing relative distances within a time-delay embedding.
  • Accommodating periodic, aperiodic, and chaotic dynamics.

Main Results:

  • Successful detection of coupling and interdependence in time series.
  • Accurate determination of coupling directionality.
  • Identification of latent coupling influenced by unobserved systems.
  • Robustness to observational noise demonstrated.

Conclusions:

  • The proposed methods offer a practical approach to analyzing coupling in deterministic nonlinear systems.
  • These techniques are applicable to simultaneous system recordings.
  • The methods are robust to noise, enhancing their utility in real-world data analysis.