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This study introduces a novel phase-based causality analysis method, outperforming amplitude-based methods in detecting weak causal links in complex systems. While phase analysis shows higher variability, it offers a powerful tool for understanding system dynamics and causality.

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Area of Science:

  • Complex Systems Science
  • Neuroscience
  • Information Theory

Background:

  • Instantaneous phases from time series reveal relationships in underlying mechanisms.
  • Phases are used for connectivity but less for causality.
  • Existing causality methods may miss subtle causal influences.

Purpose of the Study:

  • To develop a novel phase-based causality analysis method.
  • To combine mixed embedding techniques with information-theoretic causality.
  • To investigate causality in coupled oscillatory systems.

Main Methods:

  • Developed a new phase-based causality analysis technique.
  • Integrated mixed embedding and information-theoretic approaches.
  • Tested on simulated bivariate, unidirectionally coupled systems (Rössler, Lorenz, van der Pol, Mackey-Glass).

Main Results:

  • Phase-based causality detected true causal relations at lower coupling strengths than amplitude-based methods.
  • Phase analysis demonstrated higher variability, potentially due to phase extraction.
  • Successfully applied to real electroencephalographic (EEG) data for causality identification.

Conclusions:

  • Phase-based causality analysis is effective, particularly for weak causal links.
  • The method offers a valuable alternative for studying causality in complex systems.
  • Further refinement of phase extraction could improve reliability.